Factor. g^2 + 24g + 23 ____

Identify a, b, c: Identify a, b, and c in the quadratic expression g^2 + 24g + 23. The quadratic expression is in the form ag^2 + bg + c, where a = 1, b = 24, and c = 23.Find factors of c: Find two numbers that multiply to c (23) and add up to b (24). We need to find two numbers m and n such that m * n = 23 and m + n = 24. Since 23 is a prime number, the only factors of 23 are 1 and 23 itself. 1 * 23 = 23 and 1 + 23 = 24, so the numbers are 1 and 23.Write factored form: Write the factored form using the numbers found in Step 2. The factored form of the quadratic expression is (g + m)(g + n), where m = 1 and n = 23. Substitute m and n into the factored form to get (g + 1)(g + 23).

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Math Problems

Algebra 1

Factor quadratics with leading coefficient 1

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Q. Factor.

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g^2 + 24g + 23

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $g^2 + 24g + 23$ . $\newline$ The quadratic expression is in the form $ag^2 + bg + c$ , where $a = 1$ , $b = 24$ , and $b$ $0$ .
Find factors of $c$ : Find two numbers that multiply to $c$ ( $23$ ) and add up to $b$ ( $24$ ). $\newline$ We need to find two numbers $m$ and $n$ such that $m \times n = 23$ and $m + n = 24$ . $\newline$ Since $23$ is a prime number, the only factors of $23$ are $c$ $1$ and $23$ itself. $\newline$ $c$ $3$ and $c$ $4$ , so the numbers are $c$ $1$ and $23$ .
Write factored form: Write the factored form using the numbers found in Step $2$ . $\newline$ The factored form of the quadratic expression is $(g + m)(g + n)$ , where $m = 1$ and $n = 23$ . $\newline$ Substitute $m$ and $n$ into the factored form to get $(g + 1)(g + 23)$ .