Question

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

Answer 1

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

Answer 2

Answer:

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

Step-by-step 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.

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

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

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