SOLUTION: Hello, I need some help with factoring. The problem I am working on is the following: Factor completely: 8x^2 + 6x - 5 I have another problem that I need help with as well

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Hello, I need some help with factoring. The problem I am working on is the following: Factor completely: 8x^2 + 6x - 5 I have another problem that I need help with as well      Log On


   

Question 201235: Hello,
I need some help with factoring. The problem I am working on is the following:
Factor completely: 8x^2 + 6x - 5
I have another problem that I need help with as well. This one, I think is Prime, but am not totally sure.
Factor completely: x^2 + 17x+16
Any help that you can give will be greatly appreciated.
Thank you in advance for your help.
Found 2 solutions by Alan3354, jim_thompson5910:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Factor completely: 8x^2 + 6x - 5
= (4x + 5)*(2x - 1)
-------------------
I have another problem that I need help with as well. This one, I think is Prime, but am not totally sure.
Factor completely: x^2 + 17x+16
= (x+1)*(x+16)

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
# 1



Looking at the expression 8x%5E2%2B6x-5, we can see that the first coefficient is 8, the second coefficient is 6, and the last term is -5.


Now multiply the first coefficient 8 by the last term -5 to get %288%29%28-5%29=-40.


Now the question is: what two whole numbers multiply to -40 (the previous product) and add to the second coefficient 6?


To find these two numbers, we need to list all of the factors of -40 (the previous product).


Factors of -40:
1,2,4,5,8,10,20,40
-1,-2,-4,-5,-8,-10,-20,-40


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


These factors pair up and multiply to -40.
1*(-40)
2*(-20)
4*(-10)
5*(-8)
(-1)*(40)
(-2)*(20)
(-4)*(10)
(-5)*(8)

Now let's add up each pair of factors to see if one pair adds to the middle coefficient 6:


First NumberSecond NumberSum
1-401+(-40)=-39
2-202+(-20)=-18
4-104+(-10)=-6
5-85+(-8)=-3
-140-1+40=39
-220-2+20=18
-410-4+10=6
-58-5+8=3



From the table, we can see that the two numbers -4 and 10 add to 6 (the middle coefficient).


So the two numbers -4 and 10 both multiply to -40 and add to 6


Now replace the middle term 6x with -4x%2B10x. Remember, -4 and 10 add to 6. So this shows us that -4x%2B10x=6x.


8x%5E2%2Bhighlight%28-4x%2B10x%29-5 Replace the second term 6x with -4x%2B10x.


%288x%5E2-4x%29%2B%2810x-5%29 Group the terms into two pairs.


4x%282x-1%29%2B%2810x-5%29 Factor out the GCF 4x from the first group.


4x%282x-1%29%2B5%282x-1%29 Factor out 5 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.


%284x%2B5%29%282x-1%29 Combine like terms. Or factor out the common term 2x-1

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


Answer:


So 8x%5E2%2B6x-5 factors to %284x%2B5%29%282x-1%29.


Note: you can check the answer by FOILing %284x%2B5%29%282x-1%29 to get 8x%5E2%2B6x-5 or by graphing the original expression and the answer (the two graphs should be identical).




# 2




Looking at the expression x%5E2%2B17x%2B16, we can see that the first coefficient is 1, the second coefficient is 17, and the last term is 16.


Now multiply the first coefficient 1 by the last term 16 to get %281%29%2816%29=16.


Now the question is: what two whole numbers multiply to 16 (the previous product) and add to the second coefficient 17?


To find these two numbers, we need to list all of the factors of 16 (the previous product).


Factors of 16:
1,2,4,8,16
-1,-2,-4,-8,-16


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


These factors pair up and multiply to 16.
1*16
2*8
4*4
(-1)*(-16)
(-2)*(-8)
(-4)*(-4)

Now let's add up each pair of factors to see if one pair adds to the middle coefficient 17:


First NumberSecond NumberSum
1161+16=17
282+8=10
444+4=8
-1-16-1+(-16)=-17
-2-8-2+(-8)=-10
-4-4-4+(-4)=-8



From the table, we can see that the two numbers 1 and 16 add to 17 (the middle coefficient).


So the two numbers 1 and 16 both multiply to 16 and add to 17


Now replace the middle term 17x with x%2B16x. Remember, 1 and 16 add to 17. So this shows us that x%2B16x=17x.


x%5E2%2Bhighlight%28x%2B16x%29%2B16 Replace the second term 17x with x%2B16x.


%28x%5E2%2Bx%29%2B%2816x%2B16%29 Group the terms into two pairs.


x%28x%2B1%29%2B%2816x%2B16%29 Factor out the GCF x from the first group.


x%28x%2B1%29%2B16%28x%2B1%29 Factor out 16 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.


%28x%2B16%29%28x%2B1%29 Combine like terms. Or factor out the common term x%2B1

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


Answer:


So x%5E2%2B17x%2B16 factors to %28x%2B16%29%28x%2B1%29.


Note: you can check the answer by FOILing %28x%2B16%29%28x%2B1%29 to get x%5E2%2B17x%2B16 or by graphing the original expression and the answer (the two graphs should be identical).