Factor. 16p^3 - 8p^2 - 14p + 7 ______

Identify Common Factor: Look for a common factor in all terms. Check if there is a common factor that can be factored out from all terms of the polynomial 16p^3 - 8p^2 - 14p + 7. There is no common factor in all terms.Group Terms: Group terms to facilitate factoring by grouping. Group the terms into two pairs: (16p^3 - 8p^2) and (-14p + 7).Factor First Group: Factor out the common factor from the first group. Factor out the greatest common factor, which is 8p^2, from the first group (16p^3 - 8p^2). 8p^2(2p - 1)Factor Second Group: Factor out the common factor from the second group. Factor out the greatest common factor, which is -7, from the second group (-14p + 7). -7(2p - 1)Write Factored Form: Write the factored form of the polynomial. Notice that both groups now have a common binomial factor (2p - 1). Combine the factored groups using the common binomial factor. Factored form: (8p^2 - 7)(2p - 1)

Home

Math Problems

Algebra 1

Factor by grouping

Full solution

Q. Factor.

\newline

16p^3 - 8p^2 - 14p + 7

Identify Common Factor: Look for a common factor in all terms. $\newline$ Check if there is a common factor that can be factored out from all terms of the polynomial $16p^3 - 8p^2 - 14p + 7$ . $\newline$ There is no common factor in all terms.
Group Terms: Group terms to facilitate factoring by grouping. $\newline$ Group the terms into two pairs: $16p^3 - 8p^2$ and $-14p + 7$ .
Factor First Group: Factor out the common factor from the first group. $\newline$ Factor out the greatest common factor, which is $8p^2$ , from the first group $(16p^3 - 8p^2)$ . $\newline$ $8p^2(2p - 1)$
Factor Second Group: Factor out the common factor from the second group. $\newline$ Factor out the greatest common factor, which is $-7$ , from the second group $(-14p + 7)$ . $\newline$ $-7(2p - 1)$
Write Factored Form: Write the factored form of the polynomial. $\newline$ Notice that both groups now have a common binomial factor $(2p - 1)$ . $\newline$ Combine the factored groups using the common binomial factor. $\newline$ Factored form: $(8p^2 - 7)(2p - 1)$