Factor. 7m^2 + 9m + 2 ____

Identify a, b, c: Identify a, b, and c in the quadratic expression 7m^2 + 9m + 2. Compare 7m^2 + 9m + 2 with the standard form ax^2 + bx + c. a = 7 b = 9 c = 2Find numbers multiply add: Find two numbers that multiply to a*c (7*2=14) and add up to b (9). We need to find two numbers that multiply to 14 and add up to 9. The numbers are 7 and 2 because 7*2 = 14 and 7+2 = 9.Rewrite middle term: Rewrite the middle term 9m using the two numbers found in Step 2. 7m^2 + 9m + 2 can be rewritten as 7m^2 + 7m + 2m + 2.Factor by grouping: Factor by grouping. Group the first two terms and the last two terms: (7m^2 + 7m) + (2m + 2) Factor out the greatest common factor from each group: 7m(m + 1) + 2(m + 1)Factor common binomial: Factor out the common binomial factor (m + 1). The expression now looks like 7m(m + 1) + 2(m + 1). Factor out (m + 1) to get the final factored form: (m + 1)(7m + 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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7m^2 + 9m + 2

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $7m^2 + 9m + 2$ . Compare $7m^2 + 9m + 2$ with the standard form $ax^2 + bx + c$ . $a = 7$ $b$ $0$ $b$ $1$
Find numbers multiply add: Find two numbers that multiply to $a*c$ ( $7*2=14$ ) and add up to $b$ ( $9$ ). $\newline$ We need to find two numbers that multiply to $14$ and add up to $9$ . $\newline$ The numbers are $7$ and $2$ because $7*2 = 14$ and $7+2 = 9$ .
Rewrite middle term: Rewrite the middle term $9m$ using the two numbers found in Step $2$ . $7m^2 + 9m + 2$ can be rewritten as $7m^2 + 7m + 2m + 2$ .
Factor by grouping: Factor by grouping. $\newline$ Group the first two terms and the last two terms: $\newline$ $(7m^2 + 7m) + (2m + 2)$ $\newline$ Factor out the greatest common factor from each group: $\newline$ $7m(m + 1) + 2(m + 1)$
Factor common binomial: Factor out the common binomial factor $(m + 1)$ . The expression now looks like $7m(m + 1) + 2(m + 1)$ . Factor out $(m + 1)$ to get the final factored form: $(m + 1)(7m + 2)$