Question

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: Apply distributive property

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

For \( x^3 \): \( x^3 \) (only term).
For \( x^2 \): \( 3x^2 - 7x^2 = -4x^2 \).
For \( x \): \( -3x - 21x = -24x \).
Constant term: \( 21 \).

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

Answer:

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