Question

question 33 of 40
simplify the following expression:
$(x + 3) - \left(x + 2)\left(x^3 - 1\
ight)\
ight$

a. $-x^4 - 2x^3 - x + 2$
b. $-x^4 - 2x^2 + 2x + 5$
c. $-x^4 - 2x^3 + 1$
d. $-x^4 - 2x^3 + 2x + 5$

Explanation:

Step1: Expand the product term

Multiply $(x+2)(x^3 -1)$:
$x(x^3 -1) + 2(x^3 -1) = x^4 -x + 2x^3 -2 = x^4 + 2x^3 -x -2$

Step2: Subtract the expanded term

Substitute back into the original expression:
$(x + 3) - (x^4 + 2x^3 -x -2) = x + 3 -x^4 -2x^3 +x +2$

Step3: Combine like terms

Combine $x + x = 2x$ and $3 + 2 =5$:
$-x^4 -2x^3 +2x +5$

Answer:

D. $-x^4 - 2x^3 + 2x + 5$