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

• A. $3x\left(-x^2+4x-6\right)$
• B. $3x^2\left(-x^2+4x-6\right)$
• C. $3\left(-x^3+4x^2-6x\right)$
• D. $3x^2\left(-3x^4+12x^3-18x^2\right)$

Answer: (B)

Verified step by step guidance

1. Identify the terms in the polynomial: \(-3x^4 + 12x^3 - 18x^2\).
2. Determine the greatest common factor (GCF) of the coefficients: \(-3, 12,\) and \(-18\). The GCF is \(3\).
3. Identify the smallest power of \(x\) in the polynomial terms, which is \(x^2\).
4. Factor out the GCF \(3x^2\) from each term in the polynomial: \(-3x^4, 12x^3,\) and \(-18x^2\).
5. Rewrite the polynomial as \(3x^2(-x^2 + 4x - 6)\) after factoring out the GCF.