Question

What is the coefficient of $x^3$ in $(x-3)(x+2{)}^2$ ?

• A. 3
• B. 1
• C. 3
• D. 4

Answer 1

The correct option is B

1

We use the identity $(a+b{)}^2=a^2+b^2+2ab$ to expand the second term.

($x-3\left)\right(x+2{)}^2=(x-3)(x^2+4+4x)$

$=x^3+4x+4x^2-3x^2-12-12x$

$=x^3-8x+x^2-12$

The coefficient of $x^3$ in ($x-3\left)\right(x+2{)}^2$ is 1