Question

7.4 factoring polynomials using greatest common factors q

the expression \\(32x^3+40x^2+8x\\) represents total materials used. factor completely using the gcf.

\\(8x(x^2+5x+1)\\)
\\(4x(8x^2+10x+2x)\\)
\\(8x(4x^2+5x+1)\\)
\\(8x(4x^2+2x+2)\\)

Explanation:

Find the greatest common factor of the coefficients

Using the Greatest Common Factor knowledge point

$$
LATEXBLOCK0
$$

Find the greatest common factor of the variable parts

Using the Greatest Common Factor knowledge point

$$
LATEXBLOCK1
$$

Combine to find the overall GCF

Using the Greatest Common Factor knowledge point

$$ \text{Overall GCF} = 8 \cdot x = 8x $$

Factor out the GCF from each term

Using the Factoring Polynomials knowledge point

$$
LATEXBLOCK2
$$

Answer:

• (A) \(8x(x^2+5x+1)\)
• (B) \(4x(8x^2+10x+2x)\)
• (C) \(8x(4x^2+5x+1)\) (Correct answer)
• (D) \(8x(4x^2+2x+2)\)