Factor the following quadratic completely: 8r^2 - 16r - 10 Step by Step

Answer 1

8r² - 16r - 10

Notation: Standard form is Ar² + Br + C

First, divide by 2:

4r² - 8r - 5

Next, recognize that the factors of -5 have opposite signs, and therefore B will be the difference of two products.

List the possible factors of both A and C, and try the combinations for B:

(-5)*2 = -10, and 1*2 = 2, giving us -8 for B.

So:

(2r - 5)(2r + 1)(2)

CHECK by multiplying to be sure you get the original expression

Answer 2

We start with the GCF, 2.

2(4r² - 8r - 5)

Next, we multiply 4(-5) = -20. We need two factors of -20 whose sum is -8.

-4 and 5? -4 + 5 ≠ -8, so no.

-10 and 2? -10 + 2 = -8. Sweet.

2(4r² - 10r + 2r - 5)

Now, we pull out the GCF of the first two, then the last two terms.

2(2r(2r - 5) + 1(2r - 5))

Hey, we have 2r - 5 twice. If we don't end up with matching binomials, we need to try again.

Ok, just like 5w - 3w = 2w, 5(w - 5) - 3(w - 5) = 2(w - 5). We can't combine 2r and 1, though, so...

2(2r + 1)(2r - 5)

Answer 3

The easiest way to see this is to factor out the common factor of 2

2(4r²-8r-5)

The you know that 5 must be in the answer

2(2r+1)(2r-5)

Also if you don't see it right away, the quadratic formula will give you the right answer quickly as long as you know that you will need to eliminate fractions from your answer.