F(x)=4x2+8x-9 find and simplify f(2+x) a. 23+x b. 4x^2+8x-11 c. 4x^2+2x+23 d. 4x^2+24x+23

d. 4x^2 +24x +23

Step-by-step explanation:

Evaluating polynomials is sometimes easier when they are written in Horner form:

f(x) = (4x +8)x -9

Substituting (x+2) for x, we have ...

f(x+2) = (4(x+2)+8)(x+2) -9

= (4x +16)(x +2) -9

= 4x^2 +24x +32 -9

= 4x^2 +24x +23 . . . . . matches choice D

Alternative method

You can observe that the answer choices differ in the coefficient of the x-term. So, to make the correct selection, you only need to find the coefficient of the x-term. That will be the sum of coefficients of the x-terms in 4(x+2)^2 and 8(x+2). Those x-terms are 4·4x and 8x, so have a sum of (16+8)x = 24x. This matches choice D.

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