Factor. t^2 + 8t + 12 ____

Identify Coefficients: Identify the coefficients of the quadratic expression. The quadratic expression is t^2 + 8t + 12. Here, the coefficient of t^2 (a) is 1, the coefficient of t (b) is 8, and the constant term (c) is 12.Find Multiplying Numbers: Find two numbers that multiply to c (12) and add up to b (8). We need to find two numbers that multiply together to give 12 and add together to give 8. The numbers 2 and 6 satisfy these conditions because 2 * 6 = 12 and 2 + 6 = 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 (t + 2)(t + 6), because when we expand this, we get t^2 + 2t + 6t + 12, which simplifies to t^2 + 8t + 12.

Home

Math Problems

Algebra 1

Factor quadratics with leading coefficient 1

Full solution

Q. Factor.

\newline

t^2 + 8t + 12

Identify Coefficients: Identify the coefficients of the quadratic expression. $\newline$ The quadratic expression is $t^2 + 8t + 12$ . Here, the coefficient of $t^2$ ( $a$ ) is $1$ , the coefficient of $t$ ( $b$ ) is $8$ , and the constant term ( $c$ ) is $12$ .
Find Multiplying Numbers: Find two numbers that multiply to $c (12)$ and add up to $b (8)$ . $\newline$ We need to find two numbers that multiply together to give $12$ and add together to give $8$ . The numbers $2$ and $6$ satisfy these conditions because $2 \times 6 = 12$ and $2 + 6 = 8$ .
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 $(t + 2)(t + 6)$ , because when we expand this, we get $t^2 + 2t + 6t + 12$ , which simplifies to $t^2 + 8t + 12$ .