Factor. 2q^2 + 9q + 10 ____

Identify a, b, c: Identify a, b, and c in the quadratic expression 2q^2 + 9q + 10 by comparing it with the standard form ax^2 + bx + c. a = 2 b = 9 c = 10Find two numbers: Find two numbers that multiply to a*c (which is 2*10 = 20) and add up to b (which is 9). The two numbers that satisfy these conditions are 5 and 4, since 5*4 = 20 and 5+4 = 9.Rewrite middle term: Rewrite the middle term, 9q, using the two numbers found in the previous step. 2q^2 + 9q + 10 can be rewritten as 2q^2 + 5q + 4q + 10.Factor by grouping: Factor by grouping. Group the first two terms together and the last two terms together. (2q^2 + 5q) + (4q + 10)Factor out common factor: Factor out the greatest common factor from each group. From the first group, factor out q: q(2q + 5) From the second group, factor out 4: 4(2q + 5)Final factored form: Since both groups contain the common factor (2q + 5), factor this out. The factored form is (q + 4)(2q + 5).

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Math Problems

Algebra 1

Factor quadratics with other leading coefficients

Full solution

Q. Factor.

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2q^2 + 9q + 10

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $2q^2 + 9q + 10$ by comparing it with the standard form $ax^2 + bx + c$ . $\newline$ $a = 2$ $\newline$ $b = 9$ $\newline$ $b$ $0$
Find two numbers: Find two numbers that multiply to $a*c$ (which is $2*10 = 20$ ) and add up to $b$ (which is $9$ ). $\newline$ The two numbers that satisfy these conditions are $5$ and $4$ , since $5*4 = 20$ and $5+4 = 9$ .
Rewrite middle term: Rewrite the middle term, $9q$ , using the two numbers found in the previous step. $\newline$ $2q^2 + 9q + 10$ can be rewritten as $2q^2 + 5q + 4q + 10$ .
Factor by grouping: Factor by grouping. Group the first two terms together and the last two terms together. $\newline$ $(2q^2 + 5q) + (4q + 10)$
Factor out common factor: Factor out the greatest common factor from each group. $\newline$ From the first group, factor out $q$ : $q(2q + 5)$ $\newline$ From the second group, factor out $4$ : $4(2q + 5)$
Final factored form: Since both groups contain the common factor $(2q + 5)$ , factor this out. $\newline$ The factored form is $(q + 4)(2q + 5)$ .