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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)

Respuesta :

carlosego

For this case we must factor the following expression:

[tex]4x ^ 2 + 23x-72[/tex]

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

[tex]4x ^ 2 + (- 9 + 32) x-72\\4x ^ 2-9x + 32x-72[/tex]

We factor the highest common denominator of each group.

[tex]x (4x-9) +8 (4x-9)[/tex]

We factor taking into account the common term [tex](4x-9):[/tex]

[tex](4x-9) (x + 8)[/tex]

Finally, the factored expression is:

[tex](4x-9) (x + 8)[/tex]

Answer:

Option D

alinakincsem

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:

[tex]4x^2+23x-72[/tex]

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.

[tex] 4 x ^ 2 + 3 2 x - 9 x - 7 2[/tex]

[tex] 4 x ( x + 8 ) - 9 ( x + 8 ) [/tex]

[tex] ( 4 x - 9 ) ( x + 8 )[/tex]

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