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

Identify a, b, c: Identify a, b, and c in the quadratic expression 2x^2 + 9x + 7. Compare 2x^2 + 9x + 7 with ax^2 + bx + c. a = 2 b = 9 c = 7Find numbers multiply add: Find two numbers that multiply to a*c (which is 2*7=14) and add up to b (which is 9). We need to find two numbers that satisfy these conditions. After checking possible pairs that multiply to 14 (1 and 14, 2 and 7), we see that 2 and 7 add up to 9. So the two numbers are 2 and 7.Rewrite middle term: Rewrite the middle term (9x) using the two numbers found in Step 2. 2x^2 + 9x + 7 can be written as 2x^2 + 2x + 7x + 7.Factor by grouping: Factor by grouping. Group the terms into two pairs: (2x^2 + 2x) and (7x + 7). Factor out the common factor from each pair. From the first pair, factor out 2x: 2x(x + 1). From the second pair, factor out 7: 7(x + 1).Write factored form: Write the factored form of the expression. Since both groups contain the factor (x + 1), factor this out. The factored form is (2x + 7)(x + 1).

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Factor. $\newline$ $2x^2 + 9x + 7$

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Algebra 1

Factor quadratics with other leading coefficients

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Q. Factor.

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2x^2 + 9x + 7

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $2x^2 + 9x + 7$ . Compare $2x^2 + 9x + 7$ with $ax^2 + bx + c$ . $a = 2$ $b$ $0$ $b$ $1$
Find numbers multiply add: Find two numbers that multiply to $a*c$ (which is $2*7=14$ ) and add up to $b$ (which is $9$ ). $\newline$ We need to find two numbers that satisfy these conditions. $\newline$ After checking possible pairs that multiply to $14$ ( $1$ and $14$ , $2$ and $7$ ), we see that $2$ and $7$ add up to $9$ . $\newline$ So the two numbers are $2$ and $7$ .
Rewrite middle term: Rewrite the middle term $9x$ using the two numbers found in Step $2$ . $2x^2 + 9x + 7$ can be written as $2x^2 + 2x + 7x + 7$ .
Factor by grouping: Factor by grouping. $\newline$ Group the terms into two pairs: $2x^2 + 2x$ and $7x + 7$ . $\newline$ Factor out the common factor from each pair. $\newline$ From the first pair, factor out $2x$ : $2x(x + 1)$ . $\newline$ From the second pair, factor out $7$ : $7(x + 1)$ .
Write factored form: Write the factored form of the expression. $\newline$ Since both groups contain the factor $(x + 1)$ , factor this out. $\newline$ The factored form is $(2x + 7)(x + 1)$ .