Question

The diagram represents the polynomial 4x2 + 23x – 72.

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

(4x + 8)(x – 9)
(4x – 8)(x + 9)
(4x + 9)(x – 8)
(4x – 9)(x + 8)

Answer 1

The correct answer option is D. (4x – 9)(x + 8).

Explanation:

We are given the following polynomial and we are to find its factored form:

`4x^2+23x-72`

Finding factors of (-72 * 4 = ) -288 such that when added they give a result of 23 and when multiplied it gives a product of -288.

`4 x ^ 2 + 3 2 x - 9 x - 7 2`

`4 x ( x + 8 ) - 9 ( x + 8 )`

`( 4 x - 9 ) ( x + 8 )`

Answer 2

For this case we must factor the following expression:

`4x ^ 2 + 23x-72`

We rewrite the middle term as a sum of two terms whose product is
`4 * (- 72) = - 288` and whose sum is 23. These numbers are -9 and +32. So:

`4x ^ 2 + (- 9 + 32) x-72\\4x ^ 2-9x + 32x-72`

We factor the highest common denominator of each group.

`x (4x-9) +8 (4x-9)`

We factor taking into account the common term
`(4x-9):`

`(4x-9) (x + 8)`

Finally, the factored expression is:

`(4x-9) (x + 8)`

Answer:

Option D