Question

multiply the polynomials.
(x+3)(x²−6x+5)
a. x³−6x²+5x+15
b. x³−3x²+5x+15
c. x³−6x²−13x+15
d. x³−3x²−13x+15

Explanation:

Step1: Apply distributive property (FOIL for polynomials)

Multiply \( x \) by each term in \( x^2 - 6x + 5 \): \( x \cdot x^2 = x^3 \), \( x \cdot (-6x) = -6x^2 \), \( x \cdot 5 = 5x \). Then multiply \( 3 \) by each term: \( 3 \cdot x^2 = 3x^2 \), \( 3 \cdot (-6x) = -18x \), \( 3 \cdot 5 = 15 \).

Step2: Combine like terms

Combine the \( x^2 \) terms: \( -6x^2 + 3x^2 = -3x^2 \). Combine the \( x \) terms: \( 5x - 18x = -13x \). The \( x^3 \) and constant term remain. So the result is \( x^3 - 3x^2 - 13x + 15 \).

Answer:

D. \( x^3 - 3x^2 - 13x + 15 \)