Question

How do you factor `4x^2-4x-15`?

Answer 1

the answer is `(2x+3)(2x-5)`

Explanation:

for this, you have to multiply the first number and the last number so that you have to find two numbers that multiply to give you that but add yo give you the middle one. so you have to find two numbers that multiply to give you`60` and add to `-4` which is `-10,6` so now put it in the equation `4x^2-10x+6x-15` now group it `(4x^2-10x)(6x-15)` now take out. `2x(2x-5)+3(2x-5)` so now you'll left with your answer. since the inside ones are the same, you count them as one.

Answer 2

`4x^2-4x-15=color(blue)((2x+3)(2x-5)`

Explanation:

Factor:

`4x^2-4x-15`

Factor by splitting the middle term.

Multiply the coefficient of the first term `(4)` by the constant term `(-15)`.

`4xx-15=-60`

Find two factors of `-60` that add up to `-4`. The numbers `color(red)6` and `color(blue)(-10` meet the requirement.

Split `-4x` as the sum of `color(red)(6x` and `color(blue)(-10x`.

`4x^2+color(red)(6x)-color(blue)(10x)-15`

Factor out the common term from the first two terms and the second two terms.

`2x(2x+3)-5(2x+3)`

Factor out the common term `(2x+3)`.

`(2x+3)(2x-5)`