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

Identify coefficients: Identify the coefficients a, b, and c in the quadratic expression 2h^2 + 9h + 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 5 and 4 multiply to 20 and add up to 9.Rewrite middle term: Rewrite the middle term, 9h, using the two numbers found in the previous step: 5h and 4h. 2h^2 + 9h + 10 becomes 2h^2 + 5h + 4h + 10.Group terms: Group the terms into two pairs: (2h^2 + 5h) and (4h + 10).Factor out common factor: Factor out the greatest common factor from each pair. From the first pair (2h^2 + 5h), factor out h: h(2h + 5). From the second pair (4h + 10), factor out 2: 2(2h + 5).Write final expression: Notice that both groups now contain the common factor (2h + 5). Write the expression as (h + 2)(2h + 5).

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Algebra 1

Factor quadratics with other leading coefficients

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Q. Factor.

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2h^2 + 9h + 10

Identify coefficients: Identify the coefficients $a$ , $b$ , and $c$ in the quadratic expression $2h^2 + 9h + 10$ by comparing it to the standard form $ax^2 + bx + c$ . $\newline$ $a = 2$ , $b = 9$ , $c = 10$
Find two numbers: Find two numbers that multiply to $a*c$ ( $2*10 = 20$ ) and add up to $b$ ( $9$ ). $\newline$ The numbers $5$ and $4$ multiply to $20$ and add up to $9$ .
Rewrite middle term: Rewrite the middle term, $9h$ , using the two numbers found in the previous step: $5h$ and $4h$ . $\newline$ $2h^2 + 9h + 10$ becomes $2h^2 + 5h + 4h + 10$ .
Group terms: Group the terms into two pairs: $2h^2 + 5h$ and $4h + 10$ .
Factor out common factor: Factor out the greatest common factor from each pair. $\newline$ From the first pair $(2h^2 + 5h)$ , factor out $h$ : $h(2h + 5)$ . $\newline$ From the second pair $(4h + 10)$ , factor out $2$ : $2(2h + 5)$ .
Write final expression: Notice that both groups now contain the common factor $(2h + 5)$ . $\newline$ Write the expression as $(h + 2)(2h + 5)$ .