what is the factored form of 8x squared - 36x - 20

Question

what is the factored form of 8x squared - 36x - 20

 

 

Answer 1

8x² - 36x - 20

 

First off, I immediately see that all terms are

divisible by 4 so factor out a 4

 

 8x² - 36x - 20 = 4(2x² - 9x - 5)

We now need to factor 2x²-9x-5.

We can factor by grouping.  Look at the coefficient of the highest

term which is 2 on the x², and look at the constant, -5.

Multiply 2(-5) which gives us -10.

Look for factors of -10 that add to -9.  That is (-10)(1).

Replace -9x with -10x + x in the polynomial

 

2x²- 9x - 5 = 2x² - 10x + x -5

Our grouping looks like:  (2x²-10x) + (x-5)

We can factor 2x form the 1st 2 terms:

 

= 2x(x-5) + (x-5)

= (2x+1)(x-5)

 

So:

 

8x² -36x - 20 = 4(2x+1)(x-5)