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Factor out the greatest common factor. If the greatest common factor is $1$ , just retype the polynomial. $\newline$ $8p^3 + 6p$

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Factor out a monomial

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Q. Factor out the greatest common factor. If the greatest common factor is

1

, just retype the polynomial.

\newline

8p^3 + 6p

Find GCF of terms: We need to find the greatest common factor (GCF) of the terms $8p^3$ and $6p$ . To do this, we will list the prime factors of the coefficients and the common powers of $p$ . $\newline$ $8p^3 = 2^3 \times p^3$ $\newline$ $6p = 2 \times 3 \times p$ $\newline$ The common factors are $2$ and $p$ . $\newline$ GCF of $8p^3$ and $6p$ : $2p$
Express terms with GCF: Now we will express each term as the product of the GCF and the remaining factors. $\newline$ $8p^3$ can be written as $(2p) \times (4p^2)$ because $2 \times 4 \times p^2 = 8p^3$ . $\newline$ $6p$ can be written as $(2p) \times 3$ because $2 \times 3 = 6p$ .
Factor out GCF from polynomial: We can now factor out the GCF from the polynomial. $\newline$ $8p^3 + 6p$ $\newline$ = $(2p) * (4p^2) + (2p) * 3$ $\newline$ = $2p(4p^2 + 3)$ $\newline$ This is the factored form of the polynomial with the GCF factored out.

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