Factor. x^(2)+8x+12 Answer:

Identify a, b, c: Identify a, b, and c in the quadratic expression x^2 + 8x + 12. Compare x^2 + 8x + 12 with the standard quadratic form ax^2 + bx + c. Here, a = 1, b = 8, and c = 12.Find Multiplying Numbers: 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 = 12 for the product. We need two numbers that multiply to 12 and add up to 8. The numbers 2 and 6 satisfy these conditions because 2 * 6 = 12 and 2 + 6 = 8.Split Middle Term: Write the quadratic expression using the two numbers found in Step 2 to split the middle term. x^2 + 2x + 6x + 12Factor by Grouping: Factor by grouping. Group the terms to factor out common factors: (x^2 + 2x) + (6x + 12) Factor out an x from the first group and 6 from the second group: x(x + 2) + 6(x + 2)Factor Common Binomial: Factor out the common binomial factor (x + 2). (x + 2)(x + 6)

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Algebra 1

Factor quadratics with leading coefficient 1

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Q. Factor.

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x^{2}+8 x+12

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Answer:

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $x^2 + 8x + 12$ . Compare $x^2 + 8x + 12$ with the standard quadratic form $ax^2 + bx + c$ . Here, $a = 1$ , $b$ $0$ , and $b$ $1$ .
Find Multiplying Numbers: 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 $c = 12$ for the product. $\newline$ We need two numbers that multiply to $12$ and add up to $8$ . $\newline$ The numbers $2$ and $6$ satisfy these conditions because $2 \times 6 = 12$ and $a \times c$ $0$ .
Split Middle Term: Write the quadratic expression using the two numbers found in Step $2$ to split the middle term. $\newline$ $x^2 + 2x + 6x + 12$
Factor by Grouping: Factor by grouping. $\newline$ Group the terms to factor out common factors: $\newline$ $(x^2 + 2x) + (6x + 12)$ $\newline$ Factor out an $x$ from the first group and $6$ from the second group: $\newline$ $x(x + 2) + 6(x + 2)$
Factor Common Binomial: Factor out the common binomial factor $(x + 2)$ . $(x + 2)(x + 6)$