Question

in the polynomial $6x^5 - 21x^4$, which is the greatest common factor?

a) $3x$

b) $6x^4$

c) $6x^5$

d) none of these

e) $3x^4$

Explanation:

Step1: Find GCF of coefficients

Coefficients are 6 and 21. Factors of 6: 1,2,3,6. Factors of 21:1,3,7,21. GCF(6,21)=3.

Step2: Find GCF of variables

Variables: \(x^5\) and \(x^4\). For \(x\)-terms, GCF is \(x^{\min(5,4)} = x^4\).

Step3: Combine GCFs

Multiply coefficient GCF and variable GCF: \(3\times x^4 = 3x^4\).

Answer:

E. \(3x^4\)