Factor. 4s^2 + 12s + 9 ______

Identify Structure: Identify the structure of the quadratic expression; it's in the form as^2 + bs + c.Find Multiplying Numbers: Look for two numbers that multiply to ac (4 * 9 = 36) and add to b (12).Verify Numbers: The numbers 6 and 6 work because 6 * 6 = 36 and 6 + 6 = 12.Rewrite Middle Term: Rewrite the middle term using the numbers 6 and 6: 4s^2 + 6s + 6s + 9.Factor by Grouping: Factor by grouping: (4s^2 + 6s) + (6s + 9).Factor Common Factor: Factor out the common factor in each group: 2s(2s + 3) + 3(2s + 3).Factor Common Binomial: Factor out the common binomial: (2s + 3)(2s + 3).Final Factored Form: Write the final factored form as a square of a binomial: (2s + 3)^2.

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Algebra 1

Factor quadratics: special cases

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Q. Factor.

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4s^2 + 12s + 9

Identify Structure: Identify the structure of the quadratic expression; it's in the form $a s^2 + b s + c$ .
Find Multiplying Numbers: Look for two numbers that multiply to $ac$ ( $4 \times 9 = 36$ ) and add to $b$ ( $12$ ).
Verify Numbers: The numbers $6$ and $6$ work because $6 \times 6 = 36$ and $6 + 6 = 12$ .
Rewrite Middle Term: Rewrite the middle term using the numbers $6$ and $6$ : $4s^2 + 6s + 6s + 9$ .
Factor by Grouping: Factor by grouping: $(4s^2 + 6s) + (6s + 9)$ .
Factor Common Factor: Factor out the common factor in each group: $2s(2s + 3) + 3(2s + 3)$ .
Factor Common Binomial: Factor out the common binomial: \(2s + $3$ )( $2$ s + $3$ )\.
Final Factored Form: Write the final factored form as a square of a binomial: $(2s + 3)^2$ .