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

Identify coefficients: Identify the coefficients a, b, and c in the quadratic expression 2n^2 + 9n + 10 by comparing it to the standard form ax^2 + bx + c. a = 2, b = 9, c = 10Find two numbers: Find two numbers that multiply to a*c (2*10 = 20) and add up to b (9). The numbers that satisfy these conditions are 4 and 5 because 4*5 = 20 and 4+5 = 9.Rewrite middle term: Rewrite the middle term, 9n, using the two numbers found in the previous step: 4n and 5n. The expression becomes 2n^2 + 4n + 5n + 10.Factor by grouping: Factor by grouping. Group the first two terms and the last two terms separately. (2n^2 + 4n) + (5n + 10)Factor out common factor: Factor out the greatest common factor from each group. 2n(n + 2) + 5(n + 2)Final factored form: Since both groups contain the common factor (n + 2), factor it out. The factored form of the expression is (2n + 5)(n + 2).

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Math Problems

Algebra 1

Factor quadratics with other leading coefficients

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Q. Factor.

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2n^2 + 9n + 10

Identify coefficients: Identify the coefficients $a$ , $b$ , and $c$ in the quadratic expression $2n^2 + 9n + 10$ by comparing it to the standard form $ax^2 + bx + c$ . $a = 2$ , $b = 9$ , $c = 10$
Find two numbers: Find two numbers that multiply to $a*c$ ( $2*10 = 20$ ) and add up to $b$ ( $9$ ). $\newline$ The numbers that satisfy these conditions are $4$ and $5$ because $4*5 = 20$ and $4+5 = 9$ .
Rewrite middle term: Rewrite the middle term, $9n$ , using the two numbers found in the previous step: $4n$ and $5n$ . The expression becomes $2n^2 + 4n + 5n + 10$ .
Factor by grouping: Factor by grouping. Group the first two terms and the last two terms separately. $2n^2 + 4n$ + $5n + 10$
Factor out common factor: Factor out the greatest common factor from each group. $2n(n + 2) + 5(n + 2)$
Final factored form: Since both groups contain the common factor $(n + 2)$ , factor it out. $\newline$ The factored form of the expression is $(2n + 5)(n + 2)$ .