Factor. t^2 + 10t + 21 ____

Identify a, b, c: Identify a, b, and c in the quadratic expression t^2 + 10t + 21. The quadratic expression is in the standard form at^2 + bt + c. Here, a = 1, b = 10, and c = 21.Find numbers multiply and add: Find two numbers that multiply to c (21) and add up to b (10). We need to find two numbers that when multiplied give us 21 and when added give us 10. The numbers 3 and 7 satisfy these conditions because 3 * 7 = 21 and 3 + 7 = 10.Write factored form: Write the factored form using the two numbers found in Step 2. The factored form of the quadratic expression is (t + 3)(t + 7), because these two binomials multiply to give the original quadratic expression.

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Math Problems

Algebra 1

Factor quadratics with leading coefficient 1

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Q. Factor.

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t^2 + 10t + 21

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $t^2 + 10t + 21$ . $\newline$ The quadratic expression is in the standard form $at^2 + bt + c$ . Here, $a = 1$ , $b = 10$ , and $b$ $0$ .
Find numbers multiply and add: Find two numbers that multiply to $c$ ( $21$ ) and add up to $b$ ( $10$ ). $\newline$ We need to find two numbers that when multiplied give us $21$ and when added give us $10$ . The numbers $3$ and $7$ satisfy these conditions because $3 \times 7 = 21$ and $3 + 7 = 10$ .
Write factored form: Write the factored form using the two numbers found in Step $2$ . $\newline$ The factored form of the quadratic expression is $(t + 3)(t + 7)$ , because these two binomials multiply to give the original quadratic expression.