Factor. x^2 + 8x + 7 ____

Identify Coefficients: Identify the coefficients of the quadratic expression. The quadratic expression is x^2 + 8x + 7. Here, the coefficient of x^2 (a) is 1, the coefficient of x (b) is 8, and the constant term (c) is 7.Find Multiplying Numbers: Find 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 together to give 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 (x + 1)(x + 7), because these two binomials multiply to give the original quadratic expression.

Home

Math Problems

Algebra 1

Factor quadratics with leading coefficient 1

Full solution

Q. Factor.

\newline

x^2 + 8x + 7

Identify Coefficients: Identify the coefficients of the quadratic expression. $\newline$ The quadratic expression is $x^2 + 8x + 7$ . Here, the coefficient of $x^2$ ( $a$ ) is $1$ , the coefficient of $x$ ( $b$ ) is $8$ , and the constant term ( $c$ ) is $7$ .
Find Multiplying Numbers: Find 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 together to give $8$ . 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 $(x + 1)(x + 7)$ , because these two binomials multiply to give the original quadratic expression.