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Factor the polynomial by its greatest common monomial factor.

9b^(8)+24b^(3)=

Factor the polynomial by its greatest common monomial factor. $\newline$ $9 b^{8}+24 b^{3}=$

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Factor sums and differences of cubes

Full solution

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

\newline

9 b^{8}+24 b^{3}=

Identify GCF and Power: Identify the greatest common factor (GCF) of the numerical coefficients and the lowest power of the variable present in both terms. $\newline$ The numerical coefficients are $9$ and $24$ . The GCF of $9$ and $24$ is $3$ . $\newline$ The variable parts are $b^8$ and $b^3$ . The GCF of $b^8$ and $b^3$ is $b^3$ since that is the lowest power of $24$ $0$ present in both terms.
Factor Out GCF: Factor out the GCF from both terms of the polynomial. $\newline$ The GCF from step $1$ is $3b^3$ . We divide both terms of the polynomial by $3b^3$ . $\newline$ $\frac{9b^8}{3b^3} = 3b^{8-3} = 3b^5$ $\newline$ $\frac{24b^3}{3b^3} = 8b^{3-3} = 8$
Write Factored Form: Write the factored form of the polynomial using the GCF. $\newline$ The polynomial $9b^8 + 24b^3$ factored by the GCF $3b^3$ is: $\newline$ $3b^3(3b^5 + 8)$

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