Factor. t^2 + 5t + 6 ____

Identify a, b, c: Identify a, b, and c in the quadratic expression t^2 + 5t + 6. The quadratic expression is in the form at^2 + bt + c, where a = 1, b = 5, and c = 6.Find two numbers: Find two numbers that multiply to c (6) and add up to b (5). We need to find two numbers that multiply to 6 and add up to 5. The numbers 2 and 3 fit this requirement because 2 * 3 = 6 and 2 + 3 = 5.Write factored form: Write the factored form using the two numbers found in Step 2. The factored form of the quadratic expression is (t + 2)(t + 3), because when we expand this, we get t^2 + 2t + 3t + 6, which simplifies to t^2 + 5t + 6.

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Algebra 1

Factor quadratics with leading coefficient 1

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Q. Factor.

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t^2 + 5t + 6

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $t^2 + 5t + 6$ . $\newline$ The quadratic expression is in the form $at^2 + bt + c$ , where $a = 1$ , $b = 5$ , and $b$ $0$ .
Find two numbers: Find two numbers that multiply to $c$ ( $6$ ) and add up to $b$ ( $5$ ). $\newline$ We need to find two numbers that multiply to $6$ and add up to $5$ . The numbers $2$ and $3$ fit this requirement because $2 \times 3 = 6$ and $2 + 3 = 5$ .
Write factored form: Write the factored form using the two numbers found in Step $2$ . $\newline$ The factored form of the quadratic expression is $(t + 2)(t + 3)$ , because when we expand this, we get $t^2 + 2t + 3t + 6$ , which simplifies to $t^2 + 5t + 6$ .