Factor. w^2 + 8w + 7 ____

Identify Coefficients: Identify the coefficients of the quadratic expression. The quadratic expression is w^2 + 8w + 7. Here, the coefficient of w^2 (a) is 1, the coefficient of w (b) is 8, and the constant term (c) is 7.Find Multiplying Numbers: Determine two numbers that multiply to c (7) and add up to b (8). We need to find two numbers that multiply together to give 7 and add up to 8. The numbers 1 and 7 fit this requirement because 1 * 7 = 7 and 1 + 7 = 8.Write Factored Form: Write the factored form using the two numbers found in the previous step. The factored form of the quadratic expression is (w + 1)(w + 7) because these two binomials multiply to give the original quadratic expression.

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Math Problems

Algebra 1

Factor quadratics with leading coefficient 1

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Q. Factor.

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w^2 + 8w + 7

Identify Coefficients: Identify the coefficients of the quadratic expression. $\newline$ The quadratic expression is $w^2 + 8w + 7$ . Here, the coefficient of $w^2$ ( $a$ ) is $1$ , the coefficient of $w$ ( $b$ ) is $8$ , and the constant term ( $c$ ) is $7$ .
Find Multiplying Numbers: Determine two numbers that multiply to $c (7)$ and add up to $b (8)$ . We need to find two numbers that multiply together to give $7$ and add up to $8$ . The numbers $1$ and $7$ fit this requirement because $1 \times 7 = 7$ and $1 + 7 = 8$ .
Write Factored Form: Write the factored form using the two numbers found in the previous step. $\newline$ The factored form of the quadratic expression is $(w + 1)(w + 7)$ because these two binomials multiply to give the original quadratic expression.