Question

question 2.
select all the terms that are not in the product of $(x^{2}-x + 2)$ and $(x + 1)$.
a. $2$
b. $3x^{3}$
c. $3$
d. $2x^{2}$
e. $x$
f. $-2x$

Explanation:

Step1: Expand the product via distribution

$$(x^2 - x + 2)(x + 1) = x^2(x+1) - x(x+1) + 2(x+1)$$

Step2: Compute each distributed term

$$= x^3 + x^2 - x^2 - x + 2x + 2$$

Step3: Combine like terms

$$= x^3 + (x^2 - x^2) + (-x + 2x) + 2 = x^3 + x + 2$$

Step4: Identify non-present terms

Compare the expanded product $x^3 + x + 2$ to the given options to find terms not included.

Answer:

B. $3x^3$, C. $3$, D. $2x^2$, F. $-2x$