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 Radicals/195955: Rationalize the denominator 2/(square root[6] - square root [5]) If you could help me with this, i would appreciate it. 1 solutions Answer 146933 by jim_thompson5910(28593)   on 2009-05-11 23:11:06 (Show Source): You can put this solution on YOUR website! Start with the given expression. Multiply both the numerator and denominator by FOIL the denominator (use the difference of squares formula) Square each term. Combine like terms. Reduce Distribute So
 Rational-functions/195959: Divide: [(2x^2 + 5x -12)/(9x^2 - 16)]/[(2x^2 - 7x + 6)/3x^2 - x - 4)] Any help will be appreciated. Thanks1 solutions Answer 146931 by jim_thompson5910(28593)   on 2009-05-11 23:08:13 (Show Source): You can put this solution on YOUR website! Start with the given expression. Multiply the first fraction by the reciprocal of the second fraction . Factor to get . Factor to get . Factor to get . Factor to get . Combine the fractions. Highlight the common terms. Cancel out the common terms. Simplify. FOIL So simplifies to . In other words, where , , , or
 Graphs/195950: Solve: (20b^3+17b^2+18b+42)/(4b+5) 1 solutions Answer 146917 by jim_thompson5910(28593)   on 2009-05-11 21:39:06 (Show Source): You can put this solution on YOUR website!Simply use polynomial long division: Since the quotient is and the remainder is 7, this means that
 Radicals/195946: Please help me simplify this radical. 3 Square root 6 minus 3 square root 241 solutions Answer 146915 by jim_thompson5910(28593)   on 2009-05-11 21:21:56 (Show Source): You can put this solution on YOUR website! Start with the given expression Simplify to get . Multiply 3 and 2 to get 6. Combine like terms. So simplifies to . In other words,
 Radicals/195938: 2(sqrt of 3 + sqrt of 12)1 solutions Answer 146912 by jim_thompson5910(28593)   on 2009-05-11 21:13:01 (Show Source): You can put this solution on YOUR website! Start with the given expression. Distribute Factor Break up the square root Take the square root of 4 to get 2 Multiply Combine like terms. So
 Polynomials-and-rational-expressions/195928: Find P(-1/2) if P(x)= 4x^4 - 2x^3 + 171 solutions Answer 146911 by jim_thompson5910(28593)   on 2009-05-11 21:10:35 (Show Source): You can put this solution on YOUR website! Start with the given equation. Plug in . Raise to the 4th power to get . Cube to get . Multiply and to get . Multiply and to get . Combine like terms. So the answer is
 Radicals/195939: sqrt of 3(2+sqrt of 12)1 solutions Answer 146909 by jim_thompson5910(28593)   on 2009-05-11 21:04:49 (Show Source): You can put this solution on YOUR website! Start with the given expression. Distribute Rearrange the terms. Combine the roots. Multiply Take the square root of 36 to get 6 Rearrange the terms. So
 Percentage-and-ratio-word-problems/195885: Evaluate 3/4+1/21 solutions Answer 146874 by jim_thompson5910(28593)   on 2009-05-11 17:17:03 (Show Source): You can put this solution on YOUR website! So
 Square-cubic-other-roots/195883: Solve the proportion -3/4=5/x1 solutions Answer 146869 by jim_thompson5910(28593)   on 2009-05-11 17:09:02 (Show Source): You can put this solution on YOUR website! Start with the given ratio Multiply both sides by x Multiply both sides by 4 Multiply Divide both sides by -3 Reduce. So our answer is which is roughly
 Polynomials-and-rational-expressions/195843: Multiply and Simplify: 2x^2-x-3 over x^2-1 * x^2+x-2 over 2x^2 +x-61 solutions Answer 146857 by jim_thompson5910(28593)   on 2009-05-11 14:03:39 (Show Source): You can put this solution on YOUR website! Start with the given expression. Factor to get . Factor to get . Factor to get . Factor to get . Combine the fractions. Highlight the common terms. Cancel out the common terms. Simplify. So simplifies to . In other words, where , , , or
 logarithm/195840: I have a question that deals with Logarithmic Functions. I have a work sheet and the directions say to "solve". the problem is 2 with and exponet of "x" =81.1 solutions Answer 146852 by jim_thompson5910(28593)   on 2009-05-11 13:42:58 (Show Source): You can put this solution on YOUR website! Start with the given equation Take the log of both sides. Pull down the exponent. Divide both sides by Use the change of base formula So the solution is which approximates to
 Radicals/195791: Divide: 2x2 + 5x – 12 ÷ 2x2 – 7x + 6 9x2 – 16 3x2 – x – 4 Should be 2x^2+5x-12 over 9x^2-16/ 2x^2-7x+6 over 3x^2-x-4 1 solutions Answer 146843 by jim_thompson5910(28593)   on 2009-05-11 13:13:43 (Show Source): You can put this solution on YOUR website! Start with the given expression. Multiply the first fraction by the reciprocal of the second fraction . Factor to get . Factor to get . Factor to get . Factor to get . Combine the fractions. Highlight the common terms. Cancel out the common terms. Simplify. FOIL So simplifies to . In other words, where , , , , or
Polynomials-and-rational-expressions/195821: What are the factors of n^2-7n+10
1 solutions

Answer 146840 by jim_thompson5910(28593)   on 2009-05-11 13:09:13 (Show Source):
You can put this solution on YOUR website!

Looking at the expression , we can see that the first coefficient is , the second coefficient is , and the last term is .

Now multiply the first coefficient by the last term to get .

Now the question is: what two whole numbers multiply to (the previous product) and add to the second coefficient ?

To find these two numbers, we need to list all of the factors of (the previous product).

Factors of :
1,2,5,10
-1,-2,-5,-10

Note: list the negative of each factor. This will allow us to find all possible combinations.

These factors pair up and multiply to .
1*10
2*5
(-1)*(-10)
(-2)*(-5)

Now let's add up each pair of factors to see if one pair adds to the middle coefficient :

First NumberSecond NumberSum
1101+10=11
252+5=7
-1-10-1+(-10)=-11
-2-5-2+(-5)=-7

From the table, we can see that the two numbers and add to (the middle coefficient).

So the two numbers and both multiply to and add to

Now replace the middle term with . Remember, and add to . So this shows us that .

Replace the second term with .

Group the terms into two pairs.

Factor out the GCF from the first group.

Factor out from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.

Combine like terms. Or factor out the common term

---------------------------------------------

So factors to .

Note: you can check the answer by FOILing to get or by graphing the original expression and the answer (the two graphs should be identical).

Polynomials-and-rational-expressions/195822: WHat are the factors of x^2-8x+12
1 solutions

Answer 146839 by jim_thompson5910(28593)   on 2009-05-11 13:08:37 (Show Source):
You can put this solution on YOUR website!

Looking at the expression , we can see that the first coefficient is , the second coefficient is , and the last term is .

Now multiply the first coefficient by the last term to get .

Now the question is: what two whole numbers multiply to (the previous product) and add to the second coefficient ?

To find these two numbers, we need to list all of the factors of (the previous product).

Factors of :
1,2,3,4,6,12
-1,-2,-3,-4,-6,-12

Note: list the negative of each factor. This will allow us to find all possible combinations.

These factors pair up and multiply to .
1*12
2*6
3*4
(-1)*(-12)
(-2)*(-6)
(-3)*(-4)

Now let's add up each pair of factors to see if one pair adds to the middle coefficient :

First NumberSecond NumberSum
1121+12=13
262+6=8
343+4=7
-1-12-1+(-12)=-13
-2-6-2+(-6)=-8
-3-4-3+(-4)=-7

From the table, we can see that the two numbers and add to (the middle coefficient).

So the two numbers and both multiply to and add to

Now replace the middle term with . Remember, and add to . So this shows us that .

Replace the second term with .

Group the terms into two pairs.

Factor out the GCF from the first group.

Factor out from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.

Combine like terms. Or factor out the common term

---------------------------------------------

So factors to .

Note: you can check the answer by FOILing to get or by graphing the original expression and the answer (the two graphs should be identical).

 Polynomials-and-rational-expressions/195828: Please help! I need to express the following rational expression in lowest terms: x^3+5x^2 --------- 2x^2+9x-51 solutions Answer 146837 by jim_thompson5910(28593)   on 2009-05-11 13:07:39 (Show Source): You can put this solution on YOUR website!The key to these types of problems is factoring and canceling out common terms. Start with the given expression. Factor to get . Factor to get . Highlight the common terms. Cancel out the common terms. Simplify. So simplifies to . In other words, where or
 Equations/195802: I need to divide and simplify this problem. x^2-1 4x-4 ------ / ----- x^2-14x+49 x^2-2x-35 Thank you for your help!!!!!1 solutions Answer 146823 by jim_thompson5910(28593)   on 2009-05-11 11:40:02 (Show Source): You can put this solution on YOUR website! Start with the given expression. Multiply the first fraction by the reciprocal of the second fraction . Factor to get . Factor to get . Factor to get . Factor to get . Combine the fractions. Highlight the common terms. Cancel out the common terms. Simplify. FOIL Distribute So simplifies to . In other words, where , , or
 Polynomials-and-rational-expressions/195819: Please help me with the following problem. I need to express the following rational expression in lowest terms: 3x^2+18x-48 ----------- 2x+161 solutions Answer 146821 by jim_thompson5910(28593)   on 2009-05-11 11:34:53 (Show Source): You can put this solution on YOUR website! Start with the given expression. Factor to get . Factor to get . Highlight the common terms. Cancel out the common terms. Simplify. Distribute. So simplifies to . In other words, where
 Polynomials-and-rational-expressions/195811: Please help me with the following problem. I need to express the following rational expression in lowest terms: 4x^4-10x^3+8x^2 --------------- 2x1 solutions Answer 146820 by jim_thompson5910(28593)   on 2009-05-11 11:32:01 (Show Source): You can put this solution on YOUR website! Start with the given expression Factor out from the numerator Highlight the common terms. Cancel out the common terms. Simplify So where
Polynomials-and-rational-expressions/195816: What are the factors of x^2-9x+8?
1 solutions

Answer 146819 by jim_thompson5910(28593)   on 2009-05-11 11:26:54 (Show Source):
You can put this solution on YOUR website!

Looking at the expression , we can see that the first coefficient is , the second coefficient is , and the last term is .

Now multiply the first coefficient by the last term to get .

Now the question is: what two whole numbers multiply to (the previous product) and add to the second coefficient ?

To find these two numbers, we need to list all of the factors of (the previous product).

Factors of :
1,2,4,8
-1,-2,-4,-8

Note: list the negative of each factor. This will allow us to find all possible combinations.

These factors pair up and multiply to .
1*8
2*4
(-1)*(-8)
(-2)*(-4)

Now let's add up each pair of factors to see if one pair adds to the middle coefficient :

First NumberSecond NumberSum
181+8=9
242+4=6
-1-8-1+(-8)=-9
-2-4-2+(-4)=-6

From the table, we can see that the two numbers and add to (the middle coefficient).

So the two numbers and both multiply to and add to

Now replace the middle term with . Remember, and add to . So this shows us that .

Replace the second term with .

Group the terms into two pairs.

Factor out the GCF from the first group.

Factor out from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.

Combine like terms. Or factor out the common term

---------------------------------------------

So factors to .

Note: you can check the answer by FOILing to get or by graphing the original expression and the answer (the two graphs should be identical).

Polynomials-and-rational-expressions/195817: What are the factors of k^2-6k+5?
1 solutions

Answer 146818 by jim_thompson5910(28593)   on 2009-05-11 11:26:24 (Show Source):
You can put this solution on YOUR website!

Looking at the expression , we can see that the first coefficient is , the second coefficient is , and the last term is .

Now multiply the first coefficient by the last term to get .

Now the question is: what two whole numbers multiply to (the previous product) and add to the second coefficient ?

To find these two numbers, we need to list all of the factors of (the previous product).

Factors of :
1,5
-1,-5

Note: list the negative of each factor. This will allow us to find all possible combinations.

These factors pair up and multiply to .
1*5
(-1)*(-5)

Now let's add up each pair of factors to see if one pair adds to the middle coefficient :

First NumberSecond NumberSum
151+5=6
-1-5-1+(-5)=-6

From the table, we can see that the two numbers and add to (the middle coefficient).

So the two numbers and both multiply to and add to

Now replace the middle term with . Remember, and add to . So this shows us that .

Replace the second term with .

Group the terms into two pairs.

Factor out the GCF from the first group.

Factor out from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.

Combine like terms. Or factor out the common term

---------------------------------------------

So factors to .

Note: you can check the answer by FOILing to get or by graphing the original expression and the answer (the two graphs should be identical).

Polynomials-and-rational-expressions/195818: What are the factors of n^2+16n-36?
1 solutions

Answer 146817 by jim_thompson5910(28593)   on 2009-05-11 11:25:49 (Show Source):
You can put this solution on YOUR website!

Looking at the expression , we can see that the first coefficient is , the second coefficient is , and the last term is .

Now multiply the first coefficient by the last term to get .

Now the question is: what two whole numbers multiply to (the previous product) and add to the second coefficient ?

To find these two numbers, we need to list all of the factors of (the previous product).

Factors of :
1,2,3,4,6,9,12,18,36
-1,-2,-3,-4,-6,-9,-12,-18,-36

Note: list the negative of each factor. This will allow us to find all possible combinations.

These factors pair up and multiply to .
1*(-36)
2*(-18)
3*(-12)
4*(-9)
6*(-6)
(-1)*(36)
(-2)*(18)
(-3)*(12)
(-4)*(9)
(-6)*(6)

Now let's add up each pair of factors to see if one pair adds to the middle coefficient :

First NumberSecond NumberSum
1-361+(-36)=-35
2-182+(-18)=-16
3-123+(-12)=-9
4-94+(-9)=-5
6-66+(-6)=0
-136-1+36=35
-218-2+18=16
-312-3+12=9
-49-4+9=5
-66-6+6=0

From the table, we can see that the two numbers and add to (the middle coefficient).

So the two numbers and both multiply to and add to

Now replace the middle term with . Remember, and add to . So this shows us that .

Replace the second term with .

Group the terms into two pairs.

Factor out the GCF from the first group.

Factor out from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.

Combine like terms. Or factor out the common term

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