Factor. g^2 + 5g + 6 ____

Identify Coefficients: Identify the coefficients for g^2, g, and the constant term. The quadratic expression is g^2 + 5g + 6. Here, the coefficient of g^2 (a) is 1, the coefficient of g (b) is 5, and the constant term (c) is 6.Find Multiplying Numbers: Determine two numbers that multiply to c (6) and add up to b (5). We need to find two numbers that multiply together to give 6 and add together to give 5. The numbers 2 and 3 satisfy these conditions because 2 * 3 = 6 and 2 + 3 = 5.Write Factored Form: Write the factored form using the two numbers found in the previous step. The factored form of the quadratic expression is (g + 2)(g + 3), because when we expand this, we get g^2 + 2g + 3g + 6, which simplifies to g^2 + 5g + 6.

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Math Problems

Algebra 1

Factor quadratics with leading coefficient 1

Full solution

Q. Factor.

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g^2 + 5g + 6

Identify Coefficients: Identify the coefficients for $g^2$ , $g$ , and the constant term. $\newline$ The quadratic expression is $g^2 + 5g + 6$ . Here, the coefficient of $g^2$ ( $a$ ) is $1$ , the coefficient of $g$ ( $b$ ) is $5$ , and the constant term ( $c$ ) is $g$ $0$ .
Find Multiplying Numbers: Determine two numbers that multiply to $c (6)$ and add up to $b (5)$ . $\newline$ We need to find two numbers that multiply together to give $6$ and add together to give $5$ . The numbers $2$ and $3$ satisfy these conditions because $2 \times 3 = 6$ and $2 + 3 = 5$ .
Write Factored Form: Write the factored form using the two numbers found in the previous step. $\newline$ The factored form of the quadratic expression is $(g + 2)(g + 3)$ , because when we expand this, we get $g^2 + 2g + 3g + 6$ , which simplifies to $g^2 + 5g + 6$ .