Factor. j^2 + 9j + 18 ____

Identify Variables: Identify a, b, and c in the quadratic expression j^2 + 9j + 18. Compare j^2 + 9j + 18 with the standard quadratic form ax^2 + bx + c. Here, a = 1, b = 9, and c = 18.Find Product and Sum: Find two numbers that multiply to ac (which is a * c) and add up to b. Since a = 1, we only need to consider c = 18 for the product and b = 9 for the sum. We are looking for two numbers that multiply to 18 and add up to 9. The numbers 3 and 6 satisfy these conditions because 3 * 6 = 18 and 3 + 6 = 9.Split Middle Term: Write the quadratic expression using the two numbers found in Step 2 to split the middle term. j^2 + 9j + 18 can be rewritten as j^2 + 3j + 6j + 18.Factor by Grouping: Factor by grouping. Group the terms to find common factors: (j^2 + 3j) + (6j + 18). Factor out the common factor from each group: j(j + 3) + 6(j + 3).Factor Common Binomial: Factor out the common binomial factor. Since both groups contain the factor (j + 3), factor this out to get the final factored form: (j + 3)(j + 6).

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Algebra 1

Factor quadratics with leading coefficient 1

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Q. Factor.

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j^2 + 9j + 18

Identify Variables: Identify $a$ , $b$ , and $c$ in the quadratic expression $j^2 + 9j + 18$ . Compare $j^2 + 9j + 18$ with the standard quadratic form $ax^2 + bx + c$ . Here, $a = 1$ , $b = 9$ , and $c = 18$ .
Find Product and Sum: Find two numbers that multiply to $ac$ (which is $a \times c$ ) and add up to $b$ . $\newline$ Since $a = 1$ , we only need to consider $c = 18$ for the product and $b = 9$ for the sum. $\newline$ We are looking for two numbers that multiply to $18$ and add up to $9$ . $\newline$ The numbers $3$ and $6$ satisfy these conditions because $a \times c$ $0$ and $a \times c$ $1$ .
Split Middle Term: Write the quadratic expression using the two numbers found in Step $2$ to split the middle term. $j^2 + 9j + 18$ can be rewritten as $j^2 + 3j + 6j + 18$ .
Factor by Grouping: Factor by grouping. $\newline$ Group the terms to find common factors: $(j^2 + 3j) + (6j + 18)$ . $\newline$ Factor out the common factor from each group: $j(j + 3) + 6(j + 3)$ .
Factor Common Binomial: Factor out the common binomial factor. $\newline$ Since both groups contain the factor $(j + 3)$ , factor this out to get the final factored form: $(j + 3)(j + 6)$ .