Question

topic 2: simplifying polynomials

1. (x - 6)(4x² + x - 7)

Explanation:

Step1: Apply distributive property (FOIL for polynomials)

Multiply \( x \) by each term in \( 4x^2 + x - 7 \), and \(-6\) by each term in \( 4x^2 + x - 7 \):
\( x(4x^2) + x(x) + x(-7) - 6(4x^2) - 6(x) - 6(-7) \)

Step2: Simplify each term

Calculate each product:
\( 4x^3 + x^2 - 7x - 24x^2 - 6x + 42 \)

Step3: Combine like terms

Combine \( x^2 \) and \( -24x^2 \), \( -7x \) and \( -6x \):
\( 4x^3 + (1 - 24)x^2 + (-7 - 6)x + 42 \)
\( 4x^3 - 23x^2 - 13x + 42 \)

Answer:

\( 4x^3 - 23x^2 - 13x + 42 \)