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Factor the polynomial by its greatest common monomial factor.

3b^(5)+15b^(4)-18b^(7)=

Factor the polynomial by its greatest common monomial factor. $\newline$ $3 b^{5}+15 b^{4}-18 b^{7}=$

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Factor sums and differences of cubes

Full solution

Q. Factor the polynomial by its greatest common monomial factor.

\newline

3 b^{5}+15 b^{4}-18 b^{7}=

Identify GCF of coefficients and lowest power: Identify the greatest common factor (GCF) of the coefficients and the lowest power of the variable $b$ in the polynomial $3b^{5}+15b^{4}-18b^{7}$ . $\newline$ The coefficients are $3$ , $15$ , and $-18$ . The GCF of these coefficients is $3$ . $\newline$ The variable parts are $b^{5}$ , $b^{4}$ , and $b^{7}$ . The lowest power of $b$ is $b^{4}$ . $\newline$ So, the GCF of the entire polynomial is $3b^{5}+15b^{4}-18b^{7}$ $1$ .
Divide each term by GCF: Divide each term of the polynomial by the GCF to find the other factor. $\newline$ $3b^{5} \div 3b^{4} = b$ $\newline$ $15b^{4} \div 3b^{4} = 5$ $\newline$ $-18b^{7} \div 3b^{4} = -6b^{3}$
Write original polynomial as product: Write the original polynomial as the product of the GCF and the other factor. $\newline$ $3b^{5}+15b^{4}-18b^{7} = 3b^{4}(b + 5 - 6b^{3})$

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