Question

What is the factored form of 4x2 + 23x – 72?

Answer 1

4x2 + 23x – 72
= (4x - 9)(x+8)

hope that helps

Answer 2

`4x^(2) +23x-72=(4x-9)(x+8)`

Explanation:

we have

`4x^(2) +23x-72`

Equate the quadratic equation to zero

`4x^(2) +23x-72=0`

Group terms that contain the same variable, and move the constant to the opposite side of the equation

`4x^(2) +23x=72`

Factor the leading coefficient

`4(x^(2) +(23x/4))=72`

Complete the square. Remember to balance the equation by adding the same constants to each side

`4(x^(2) +(23x/4)+(529/64))=72+(529/16)`

`4(x^(2) +(23x/4)+(529/64))=1681/16`

`(x^(2) +(23x/4)+(529/64))=1681/64`

Rewrite as perfect squares

`(x+(23/8))^(2)=1681/64`

square root both sides

`(x+(23/8))=(+/-)41/8`

`x=-(23/8)(+/-)41/8`

`x=-(23/8)+41/8=18/8=9/4`

`x=-(23/8)-41/8=-64/8=-8`

therefore

`4x^(2) +23x-72=4(x-9/4)(x+8)`

`4x^(2) +23x-72=(4x-9)(x+8)`