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Factor. $\newline$ $2k^2 + 9k + 10$

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Factor quadratics with other leading coefficients

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Q. Factor.

\newline

2k^2 + 9k + 10

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $2k^2 + 9k + 10$ . Compare $2k^2 + 9k + 10$ with $ax^2 + bx + c$ . $a = 2$ $b$ $0$ $b$ $1$
Find Numbers Multiply Add: Find two numbers that multiply to $a*c$ ( $2*10 = 20$ ) and add up to $b$ ( $9$ ). $\newline$ We need to find two numbers that multiply to $20$ and add up to $9$ . $\newline$ The numbers $4$ and $5$ satisfy these conditions because $4*5 = 20$ and $4+5 = 9$ .
Rewrite Middle Term: Rewrite the middle term $9k$ using the two numbers found in Step $2$ . $2k^2 + 9k + 10$ can be rewritten as $2k^2 + 4k + 5k + 10$ .
Factor by Grouping: Factor by grouping. $\newline$ Group the first two terms and the last two terms: $\newline$ $(2k^2 + 4k) + (5k + 10)$ $\newline$ Factor out the common factor from each group: $\newline$ $2k(k + 2) + 5(k + 2)$
Factor Common Binomial: Factor out the common binomial factor. $\newline$ Both groups contain the common factor $(k + 2)$ , so factor this out: $\newline$ $(2k + 5)(k + 2)$

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