Factor. 2p^2 + 23p + 11 ____

Identify coefficients: Identify the coefficients a, b, and c in the quadratic expression 2p^2 + 23p + 11 by comparing it to the standard form ax^2 + bx + c. a = 2, b = 23, c = 11.Find suitable numbers: Find two numbers that multiply to a*c (which is 2*11 = 22) and add up to b (which is 23). The numbers that satisfy these conditions are 1 and 22 because 1*22 = 22 and 1+22 = 23.Rewrite middle term: Rewrite the middle term 23p using the two numbers found in the previous step. 2p^2 + 23p + 11 can be rewritten as 2p^2 + 1p + 22p + 11.Group and factor: Group the terms into two pairs and factor by grouping. Group (2p^2 + 1p) and (22p + 11). Factor out the greatest common factor from each group. From the first group, factor out p: p(2p + 1). From the second group, factor out 11: 11(2p + 1).Factor out common factor: Notice that both groups now have a common factor of (2p + 1). Factor out the common factor to get the final factored form. The factored form is (p + 11)(2p + 1).

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Algebra 1

Factor quadratics with other leading coefficients

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Q. Factor.

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2p^2 + 23p + 11

Identify coefficients: Identify the coefficients $a$ , $b$ , and $c$ in the quadratic expression $2p^2 + 23p + 11$ by comparing it to the standard form $ax^2 + bx + c$ . $a = 2$ , $b = 23$ , $c = 11$ .
Find suitable numbers: Find two numbers that multiply to $a*c$ (which is $2*11 = 22$ ) and add up to $b$ (which is $23$ ). $\newline$ The numbers that satisfy these conditions are $1$ and $22$ because $1*22 = 22$ and $1+22 = 23$ .
Rewrite middle term: Rewrite the middle term $23p$ using the two numbers found in the previous step. $2p^2 + 23p + 11$ can be rewritten as $2p^2 + 1p + 22p + 11$ .
Group and factor: Group the terms into two pairs and factor by grouping. $\newline$ Group $2p^2 + 1p$ and $22p + 11$ . $\newline$ Factor out the greatest common factor from each group. $\newline$ From the first group, factor out $p$ : $p(2p + 1)$ . $\newline$ From the second group, factor out $11$ : $11(2p + 1)$ .
Factor out common factor: Notice that both groups now have a common factor of $2p + 1$ . Factor out the common factor to get the final factored form. The factored form is $p + 11$ ( $2$ p + $1$ \).