Factor. j^2 + 24j + 23 ______

Identify Variables: Identify a, b, and c in the quadratic expression j^2 + 24j + 23. Compare j^2 + 24j + 23 with the standard quadratic form ax^2 + bx + c. Here, a = 1, b = 24, and c = 23.Find Product and Sum: Find two numbers whose product is a*c (which is 23) and whose sum is b (which is 24). We need to find two numbers that multiply to 23 and add up to 24. The numbers 1 and 23 satisfy these conditions because: 1 * 23 = 23 (product) 1 + 23 = 24 (sum)Write Factored Form: Write the factored form using the two numbers found in Step 2. The factored form of the quadratic expression is (j + 1)(j + 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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j^2 + 24j + 23

Identify Variables: Identify $a$ , $b$ , and $c$ in the quadratic expression $j^2 + 24j + 23$ . Compare $j^2 + 24j + 23$ with the standard quadratic form $ax^2 + bx + c$ . Here, $a = 1$ , $b = 24$ , and $c = 23$ .
Find Product and Sum: Find two numbers whose product is $a*c$ (which is $23$ ) and whose sum is $b$ (which is $24$ ). $\newline$ We need to find two numbers that multiply to $23$ and add up to $24$ . $\newline$ The numbers $1$ and $23$ satisfy these conditions because: $\newline$ $1 \times 23 = 23$ (product) $\newline$ $1 + 23 = 24$ (sum)
Write Factored Form: Write the factored form using the two numbers found in Step $2$ . $\newline$ The factored form of the quadratic expression is $(j + 1)(j + 23)$ .