Factor. j^2 + 8j + 7 ____

Identify Coefficients: Identify the coefficients for j^2, j, and the constant term in the quadratic expression j^2 + 8j + 7. Comparing j^2 + 8j + 7 with the standard quadratic form ax^2 + bx + c, we find that a = 1 (coefficient of j^2), b = 8 (coefficient of j), and c = 7 (constant term).Find Multiplying Numbers: Determine two numbers that multiply to give c (7) and add up to give b (8). We are looking for two numbers that when multiplied give 7 and when added give 8. The numbers 1 and 7 satisfy these conditions 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 (j + 1)(j + 7), because these factors will multiply to give the original quadratic expression j^2 + 8j + 7.

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Math Problems

Algebra 1

Factor quadratics with leading coefficient 1

Full solution

Q. Factor.

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j^2 + 8j + 7

Identify Coefficients: Identify the coefficients for $j^2$ , $j$ , and the constant term in the quadratic expression $j^2 + 8j + 7$ . Comparing $j^2 + 8j + 7$ with the standard quadratic form $ax^2 + bx + c$ , we find that $a = 1$ (coefficient of $j^2$ ), $b = 8$ (coefficient of $j$ ), and $c = 7$ (constant term).
Find Multiplying Numbers: Determine two numbers that multiply to give $c (7)$ and add up to give $b (8)$ . We are looking for two numbers that when multiplied give $7$ and when added give $8$ . The numbers $1$ and $7$ satisfy these conditions 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 $(j + 1)(j + 7)$ , because these factors will multiply to give the original quadratic expression $j^2 + 8j + 7$ .