Factor. v^2 + 8v + 15 ____

Identify Coefficients: Identify the coefficients of the quadratic expression. The quadratic expression is v^2 + 8v + 15. Here, the coefficient of v^2 (a) is 1, the coefficient of v (b) is 8, and the constant term (c) is 15.Find Multiplying Numbers: Find two numbers that multiply to c (15) and add up to b (8). We need to find two numbers that multiply together to give 15 and add together to give 8. The numbers 3 and 5 satisfy these conditions because 3 * 5 = 15 and 3 + 5 = 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 (v + 3)(v + 5), because when we expand this, we get v^2 + 3v + 5v + 15, which simplifies to v^2 + 8v + 15.

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Math Problems

Algebra 1

Factor quadratics with leading coefficient 1

Full solution

Q. Factor.

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v^2 + 8v + 15

Identify Coefficients: Identify the coefficients of the quadratic expression. $\newline$ The quadratic expression is $v^2 + 8v + 15$ . Here, the coefficient of $v^2$ ( $a$ ) is $1$ , the coefficient of $v$ ( $b$ ) is $8$ , and the constant term ( $c$ ) is $15$ .
Find Multiplying Numbers: Find two numbers that multiply to $c (15)$ and add up to $b (8)$ . $\newline$ We need to find two numbers that multiply together to give $15$ and add together to give $8$ . The numbers $3$ and $5$ satisfy these conditions because $3 \times 5 = 15$ and $3 + 5 = 8$ .
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 $(v + 3)(v + 5)$ , because when we expand this, we get $v^2 + 3v + 5v + 15$ , which simplifies to $v^2 + 8v + 15$ .