Factor. g^2 + 10g + 16 ____

Identify a, b, c: Identify a, b, and c in the quadratic expression g^2 + 10g + 16. Compare g^2 + 10g + 16 with the standard quadratic form ax^2 + bx + c. Here, a = 1, b = 10, and c = 16.Find factor pairs: Find two numbers that multiply to c (16) and add up to b (10). We need to find two numbers m and n such that m * n = 16 and m + n = 10.List and add pairs: List the pairs of factors of 16 and find the pair that adds up to 10. The pairs of factors of 16 are (1, 16), (2, 8), and (4, 4). The pair that adds up to 10 is (2, 8) because 2 + 8 = 10.Write factored form: Write the factored form using the numbers found in Step 3. The factored form of the quadratic expression is (g + 2)(g + 8).

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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 + 10g + 16

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $g^2 + 10g + 16$ . Compare $g^2 + 10g + 16$ with the standard quadratic form $ax^2 + bx + c$ . Here, $a = 1$ , $b$ $0$ , and $b$ $1$ .
Find factor pairs: Find two numbers that multiply to $c (16)$ and add up to $b (10)$ . We need to find two numbers $m$ and $n$ such that $m \times n = 16$ and $m + n = 10$ .
List and add pairs: List the pairs of factors of $16$ and find the pair that adds up to $10$ . The pairs of factors of $16$ are $(1, 16)$ , $(2, 8)$ , and $(4, 4)$ . The pair that adds up to $10$ is $(2, 8)$ because $2 + 8 = 10$ .
Write factored form: Write the factored form using the numbers found in Step $3$ . $\newline$ The factored form of the quadratic expression is $(g + 2)(g + 8)$ .