Question

1 fill in the blank 7 points multiply the polynomials. (x - 3)(x² + 8x + 1) answer: axᵇ + cxᵈ + exᶠ + g a = type your answer... b = type your answer... c = type your answer... d = type your answer... e = type your answer... f = type your answer... g = type your answer...

Explanation:

Step1: Apply distributive property (FOIL extended)

Multiply \( x \) by each term in \( x^2 + 8x + 1 \): \( x \cdot x^2 = x^3 \), \( x \cdot 8x = 8x^2 \), \( x \cdot 1 = x \).
Multiply \( -3 \) by each term in \( x^2 + 8x + 1 \): \( -3 \cdot x^2 = -3x^2 \), \( -3 \cdot 8x = -24x \), \( -3 \cdot 1 = -3 \).

Step2: Combine like terms

For \( x^3 \): only \( x^3 \), so coefficient \( a = 1 \), exponent \( b = 3 \).
For \( x^2 \): \( 8x^2 - 3x^2 = 5x^2 \), so coefficient \( c = 5 \), exponent \( d = 2 \).
For \( x \): \( x - 24x = -23x \), so coefficient \( e = -23 \), exponent \( f = 1 \).
Constant term: \( -3 \), so \( g = -3 \).

Answer:

\( a = 1 \), \( b = 3 \), \( c = 5 \), \( d = 2 \), \( e = -23 \), \( f = 1 \), \( g = -3 \)