Factor. j^2 + 6j + 5 ____

Identify Variables: Identify a, b, and c in the quadratic expression j^2 + 6j + 5. The quadratic expression is in the form j^2 + bj + c, where a = 1 (the coefficient of j^2), b = 6 (the coefficient of j), and c = 5 (the constant term).Find Multiplying Numbers: Find two numbers that multiply to c (5) and add up to b (6). We need to find two numbers that multiply together to give 5 and when added together give 6. The numbers 1 and 5 satisfy these conditions because 1 * 5 = 5 and 1 + 5 = 6.Write Factored Form: Write the factored form using the two numbers found in Step 2. The factored form of the quadratic expression is (j + 1)(j + 5), because when we apply the distributive property (FOIL), we get back the original expression: j^2 + 5j + 1j + 5, which simplifies to j^2 + 6j + 5.

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Math Problems

Algebra 1

Factor quadratics with leading coefficient 1

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Q. Factor.

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j^2 + 6j + 5

Identify Variables: Identify $a$ , $b$ , and $c$ in the quadratic expression $j^2 + 6j + 5$ . The quadratic expression is in the form $j^2 + bj + c$ , where $a = 1$ (the coefficient of $j^2$ ), $b = 6$ (the coefficient of $j$ ), and $c = 5$ (the constant term).
Find Multiplying Numbers: Find two numbers that multiply to $c (5)$ and add up to $b (6)$ . We need to find two numbers that multiply together to give $5$ and when added together give $6$ . The numbers $1$ and $5$ satisfy these conditions because $1 \times 5 = 5$ and $1 + 5 = 6$ .
Write Factored Form: Write the factored form using the two numbers found in Step $2$ . $\newline$ The factored form of the quadratic expression is $(j + 1)(j + 5)$ , because when we apply the distributive property (FOIL), we get back the original expression: $j^2 + 5j + 1j + 5$ , which simplifies to $j^2 + 6j + 5$ .