Question

question 2 of 10
multiply the polynomials.
(x - 7)(x² + 3x - 3)

a. x³ - 4x² - 3x + 21
b. x³ - 7x² - 3x + 21
c. x³ - 4x² - 24x + 21
d. x³ - 7x² - 24x + 21

Explanation:

Step1: Distribute \(x\) and \(-7\)

Multiply \(x\) with each term in \((x^2 + 3x - 3)\): \(x \cdot x^2 = x^3\), \(x \cdot 3x = 3x^2\), \(x \cdot (-3) = -3x\).
Multiply \(-7\) with each term in \((x^2 + 3x - 3)\): \(-7 \cdot x^2 = -7x^2\), \(-7 \cdot 3x = -21x\), \(-7 \cdot (-3) = 21\).

Step2: Combine like terms

Combine the \(x^2\) terms: \(3x^2 - 7x^2 = -4x^2\).
Combine the \(x\) terms: \(-3x - 21x = -24x\).

Step3: Write the expanded polynomial

Put all terms together: \(x^3 - 4x^2 - 24x + 21\).

Answer:

C. \(x^3 - 4x^2 - 24x + 21\)