Question

the variables a, b, and c represent polynomials where a = x², b = 3x + 2, and c = x - 3. what is ab - c in simplest form?\
\bigcirc 3x³ + 2x² - x + 3\
\bigcirc 3x³ + 2x² - x - 3\
\bigcirc 3x³ + x² - 6x + 9\
\bigcirc 3x³ + x² + 6x - 9

Explanation:

Step1: Calculate $AB$

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

Step2: Calculate $C^2$

$C^2 = (x - 3)^2 = x^2 - 6x + 9$

Step3: Compute $AB - C^2$

$AB - C^2 = (3x^3 + 2x^2) - (x^2 - 6x + 9) = 3x^3 + 2x^2 - x^2 + 6x - 9 = 3x^3 + x^2 + 6x - 9$

Answer:

$\boldsymbol{3x^3 + x^2 + 6x - 9}$ (corresponding to the last option)