Factor. d^2 + 10d + 21 ____

Identify b and c: Identify b and c in the quadratic expression d^2 + 10d + 21. Compare d^2 + 10d + 21 with the standard quadratic form x^2 + bx + c. Here, b = 10 and c = 21.Find two numbers: Find two numbers whose product is c (21) and whose sum is b (10). We need to find two numbers that multiply to 21 and add up to 10. The numbers 3 and 7 satisfy these conditions because: 3 * 7 = 21 (product is 21) 3 + 7 = 10 (sum is 10)Write factored form: Write the factored form using the two numbers found in Step 2. The quadratic expression d^2 + 10d + 21 can be factored as (d + 3)(d + 7).

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Math Problems

Algebra 1

Factor quadratics with leading coefficient 1

Full solution

Q. Factor.

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d^2 + 10d + 21

Identify $b$ and $c$ : Identify $b$ and $c$ in the quadratic expression $d^2 + 10d + 21$ . Compare $d^2 + 10d + 21$ with the standard quadratic form $x^2 + bx + c$ . Here, $b = 10$ and $c = 21$ .
Find two numbers: Find two numbers whose product is $c$ $(21)$ and whose sum is $b$ $(10)$ . We need to find two numbers that multiply to $21$ and add up to $10$ . The numbers $3$ and $7$ satisfy these conditions because: $3 \times 7 = 21$ (product is $21$ ) $(21)$ $0$ (sum is $10$ )
Write factored form: Write the factored form using the two numbers found in Step $2$ . $\newline$ The quadratic expression $d^2 + 10d + 21$ can be factored as $(d + 3)(d + 7)$ .