0. Review of Algebra

Factoring Polynomials

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Multiple Choice

Factor out the Greatest Common Factor in the polynomial.
$-3x^4+12x^3-18x^2$

$3x\left(-x^2+4x-6\right)$

$3x^2\left(-x^2+4x-6\right)$

$3\left(-x^3+4x^2-6x\right)$

$3x^2\left(-3x^4+12x^3-18x^2\right)$

Verified step by step guidance

Identify the terms in the polynomial: $-3x^4 + 12x^3 - 18x^2$.

Determine the greatest common factor (GCF) of the coefficients: $-3, 12,$ and $-18$. The GCF is $3$.

Identify the smallest power of $x$ in the polynomial terms, which is $x^2$.

Factor out the GCF $3x^2$ from each term in the polynomial: $-3x^4, 12x^3,$ and $-18x^2$.

Rewrite the polynomial as $3x^2(-x^2 + 4x - 6)$ after factoring out the GCF.

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Expert video explanations

Factor out the Greatest Common Factor in the polynomial.−3x4+12x3−18x2-3x^4+12x^3-18x^2−3x4+12x3−18x2