SOLUTION: Factor each expression completely. 1. 12x2 + 6x + 18 3(2x2 + x + 3) 6(2x2 + x + 3) 3(2x – 1)(x + 3) 6(2x – 1)(x + 3) 2. m2 + 11m + 18 (m – 2)(m + 9) (m

Algebra ->  Distributive-associative-commutative-properties -> SOLUTION: Factor each expression completely. 1. 12x2 + 6x + 18 3(2x2 + x + 3) 6(2x2 + x + 3) 3(2x – 1)(x + 3) 6(2x – 1)(x + 3) 2. m2 + 11m + 18 (m – 2)(m + 9) (m      Log On


   

Question 171535:

Factor each expression completely.
1. 12x2 + 6x + 18
3(2x2 + x + 3)
6(2x2 + x + 3)
3(2x – 1)(x + 3)
6(2x – 1)(x + 3)
2. m2 + 11m + 18
(m – 2)(m + 9)
(m + 2)(m + 9)
(m – 3)(m + 6)
(m + 3)(m + 6)
3. x2 – 14x – 15
(x – 5)(x + 3)
(x + 5)(x – 3)
(x – 15)(x + 1)
(x + 15)(x – 1)
4. x2 – 13x + 42
(x + 6)(x – 7)
(x – 6)(x + 7)
(x – 6)(x – 7)
(x + 6)(x + 7)
5. 64x2 + 144x + 81
(8x – 9)2
(8x + 9)2
2(8x + 9)
(8x + 9)(8x – 9)
6. 3x2 + 5x – 50
(x – 25)(3x + 2)
(3x – 25)(x + 2)
(x – 10)(3x + 5)
(3x – 10)(x + 5)
7. 5k2 – 125
(k – 5)2
5(k – 5)2
(k + 5)(k – 5)
5(k + 5)(k – 5)
8. 15n2 – 8n +1
(5n + 1)(3n + 1)
(5n – 1)(3n – 1)
(5n + 1)(3n – 1)
(5n – 1)(3n + 1)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first three to get you started


# 1




12x%5E2%2B6x%2B18 Start with the given expression


6%282x%5E2%2Bx%2B3%29 Factor out the GCF 6


Now let's focus on the inner expression 2x%5E2%2Bx%2B3




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Looking at 2x%5E2%2B1x%2B3 we can see that the first term is 2x%5E2 and the last term is 3 where the coefficients are 2 and 3 respectively.

Now multiply the first coefficient 2 and the last coefficient 3 to get 6. Now what two numbers multiply to 6 and add to the middle coefficient 1? Let's list all of the factors of 6:



Factors of 6:
1,2,3,6

-1,-2,-3,-6 ...List the negative factors as well. This will allow us to find all possible combinations

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

note: remember two negative numbers multiplied together make a positive number


Now which of these pairs add to 1? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 1

First NumberSecond NumberSum
161+6=7
232+3=5
-1-6-1+(-6)=-7
-2-3-2+(-3)=-5

None of these pairs of factors add to 1. So the expression 2x%5E2%2Bx%2B3 cannot be factored


So 6%282x%5E2%2Bx%2B3%29 just remains as 6%282x%5E2%2Bx%2B3%29

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Answer:

So 12x%5E2%2B6x%2B18 factors to 6%282x%5E2%2Bx%2B3%29






# 2




Looking at 1m%5E2%2B11m%2B18 we can see that the first term is 1m%5E2 and the last term is 18 where the coefficients are 1 and 18 respectively.

Now multiply the first coefficient 1 and the last coefficient 18 to get 18. Now what two numbers multiply to 18 and add to the middle coefficient 11? Let's list all of the factors of 18:



Factors of 18:
1,2,3,6,9,18

-1,-2,-3,-6,-9,-18 ...List the negative factors as well. This will allow us to find all possible combinations

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

note: remember two negative numbers multiplied together make a positive number


Now which of these pairs add to 11? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 11

First NumberSecond NumberSum
1181+18=19
292+9=11
363+6=9
-1-18-1+(-18)=-19
-2-9-2+(-9)=-11
-3-6-3+(-6)=-9



From this list we can see that 2 and 9 add up to 11 and multiply to 18


Now looking at the expression 1m%5E2%2B11m%2B18, replace 11m with 2m%2B9m (notice 2m%2B9m adds up to 11m. So it is equivalent to 11m)

1m%5E2%2Bhighlight%282m%2B9m%29%2B18


Now let's factor 1m%5E2%2B2m%2B9m%2B18 by grouping:


%281m%5E2%2B2m%29%2B%289m%2B18%29 Group like terms


m%28m%2B2%29%2B9%28m%2B2%29 Factor out the GCF of m out of the first group. Factor out the GCF of 9 out of the second group


%28m%2B9%29%28m%2B2%29 Since we have a common term of m%2B2, we can combine like terms

So 1m%5E2%2B2m%2B9m%2B18 factors to %28m%2B9%29%28m%2B2%29


So this also means that 1m%5E2%2B11m%2B18 factors to %28m%2B9%29%28m%2B2%29 (since 1m%5E2%2B11m%2B18 is equivalent to 1m%5E2%2B2m%2B9m%2B18)



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Answer:
So m%5E2%2B11m%2B18 factors to %28m%2B9%29%28m%2B2%29







# 3



Looking at 1x%5E2-14x-15 we can see that the first term is 1x%5E2 and the last term is -15 where the coefficients are 1 and -15 respectively.

Now multiply the first coefficient 1 and the last coefficient -15 to get -15. Now what two numbers multiply to -15 and add to the middle coefficient -14? Let's list all of the factors of -15:



Factors of -15:
1,3,5,15

-1,-3,-5,-15 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to -15
(1)*(-15)
(3)*(-5)
(-1)*(15)
(-3)*(5)

note: remember, the product of a negative and a positive number is a negative number


Now which of these pairs add to -14? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -14

First NumberSecond NumberSum
1-151+(-15)=-14
3-53+(-5)=-2
-115-1+15=14
-35-3+5=2



From this list we can see that 1 and -15 add up to -14 and multiply to -15


Now looking at the expression 1x%5E2-14x-15, replace -14x with 1x%2B-15x (notice 1x%2B-15x adds up to -14x. So it is equivalent to -14x)

1x%5E2%2Bhighlight%281x%2B-15x%29%2B-15


Now let's factor 1x%5E2%2B1x-15x-15 by grouping:


%281x%5E2%2B1x%29%2B%28-15x-15%29 Group like terms


x%28x%2B1%29-15%28x%2B1%29 Factor out the GCF of x out of the first group. Factor out the GCF of -15 out of the second group


%28x-15%29%28x%2B1%29 Since we have a common term of x%2B1, we can combine like terms

So 1x%5E2%2B1x-15x-15 factors to %28x-15%29%28x%2B1%29


So this also means that 1x%5E2-14x-15 factors to %28x-15%29%28x%2B1%29 (since 1x%5E2-14x-15 is equivalent to 1x%5E2%2B1x-15x-15)



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Answer:
So x%5E2-14x-15 factors to %28x-15%29%28x%2B1%29