Factor. 2w^2 + 18w + 36 ____

Identify Common Factor: First, look for a common factor in all terms. 2w^2, 18w, and 36 all have a common factor of 2. Factor out the 2: 2(w^2 + 9w + 18).Factor Quadratic Inside: Now, factor the quadratic inside the parentheses. We need two numbers that multiply to 18 (the constant term) and add up to 9 (the coefficient of w). The numbers 3 and 6 work: 3 * 6 = 18 and 3 + 6 = 9.Write Factored Form: Write the factored form using the numbers 3 and 6. 2(w + 3)(w + 6) is the factored form of the quadratic.Check Factored Form: Check the factored form by expanding it to see if we get the original expression. 2(w + 3)(w + 6) = 2(w^2 + 6w + 3w + 18) = 2w^2 + 12w + 6w + 36 = 2w^2 + 18w + 36. It matches the original expression, so the factoring is correct.

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Q. Factor.

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2w^2 + 18w + 36

Identify Common Factor: First, look for a common factor in all terms. $2w^2$ , $18w$ , and $36$ all have a common factor of $2$ . Factor out the $2$ : $2(w^2 + 9w + 18)$ .
Factor Quadratic Inside: Now, factor the quadratic inside the parentheses. $\newline$ We need two numbers that multiply to $18$ (the constant term) and add up to $9$ (the coefficient of $w$ ). $\newline$ The numbers $3$ and $6$ work: $3 \times 6 = 18$ and $3 + 6 = 9$ .
Write Factored Form: Write the factored form using the numbers $3$ and $6$ . $2(w + 3)(w + 6)$ is the factored form of the quadratic.
Check Factored Form: Check the factored form by expanding it to see if we get the original expression. $\newline$ $2(w + 3)(w + 6) = 2(w^2 + 6w + 3w + 18) = 2w^2 + 12w + 6w + 36 = 2w^2 + 18w + 36$ . $\newline$ It matches the original expression, so the factoring is correct.