Factor. 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 = 9 c = 10Find Numbers Multiply Add: Find two numbers that multiply to a*c (2*10 = 20) and add up to b (9). We need to find two numbers that multiply to 20 and add up to 9. 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. Group the first two terms and the last two terms: (2k^2 + 4k) + (5k + 10) Factor out the common factor from each group: 2k(k + 2) + 5(k + 2)Factor Common Binomial: Factor out the common binomial factor. Both groups contain the common factor (k + 2), so factor this out: (2k + 5)(k + 2)

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Algebra 1

Factor quadratics with other leading coefficients

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Q. Factor.

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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: $\newline$ $(2k + 5)(k + 2)$