Factor. d^2 + 18d + 17 ____

Identify b and c: Identify b and c in the quadratic expression d^2 + 18d + 17. Compare d^2 + 18d + 17 with the standard quadratic form x^2 + bx + c. Here, b = 18 and c = 17.Find product and sum: Find two numbers whose product is c (17) and whose sum is b (18). We need to find two numbers that multiply to 17 and add up to 18. Since 17 is a prime number, the only factors of 17 are 1 and 17 itself. 1 * 17 = 17 and 1 + 17 = 18, which matches our requirements. Two numbers: 1, 17.Write factored form: Write the factored form using the two numbers found in Step 2. The factored form of the quadratic expression is (d + 1)(d + 17).

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Math Problems

Algebra 1

Factor quadratics with leading coefficient 1

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Q. Factor.

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d^2 + 18d + 17

Identify $b$ and $c$ : Identify $b$ and $c$ in the quadratic expression $d^2 + 18d + 17$ . Compare $d^2 + 18d + 17$ with the standard quadratic form $x^2 + bx + c$ . Here, $b = 18$ and $c = 17$ .
Find product and sum: Find two numbers whose product is $c$ $(17)$ and whose sum is $b$ $(18)$ . We need to find two numbers that multiply to $17$ and add up to $18$ . Since $17$ is a prime number, the only factors of $17$ are $1$ and $17$ itself. $(17)$ $0$ and $(17)$ $1$ , which matches our requirements. Two numbers: $1$ , $17$ .
Write factored form: Write the factored form using the two numbers found in Step $2$ . $\newline$ The factored form of the quadratic expression is $(d + 1)(d + 17)$ .