Question

Factor each polynomial
4z^2+4z-15

Answer 1

(2z+5) (2z-3)

Explanation:

First, multiply the first coefficient by the third.

4*-15=-60

Then find factors of -60 that add up to the middle term.

The factors are: -6 and 10-------> -6*10=-60 and -6+10=4 so -6 and 10 are the correct factors.

Break up the middle term with the factors that you got above. The new equation will be: 4
`z^(2)`-6z+10z-15

Factor by grouping.

First, break the equation into two

(4
`z^(2)`-6z) (10z-15)

Then, factor out the greatest number you can

2z(2z-3) 5(2z-3)

You are then left with a common binomial of 2z-3. COmbine the common binomial into 1 and combine the 2 numbers you factored out in the step above (2z and 5) The final equation will be this:

(2z+5) (2z-3)

Answer 2

(2z + 5)(2z - 3)

Explanation:

4z² + 4z - 15

4z² + 10z - 6z - 15

2z (2z + 5) - 3 (2z + 5)

(2z + 5)(2z - 3)