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Factor. $\newline$ $16q^2 + 24q + 9$

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Factor quadratics: special cases

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Q. Factor.

\newline

16q^2 + 24q + 9

Check Perfect Square Trinomial: Determine if the quadratic expression can be factored as a perfect square trinomial. $\newline$ A perfect square trinomial is in the form $(a + b)^2 = a^2 + 2ab + b^2$ . We need to check if $16q^2 + 24q + 9$ fits this pattern. $\newline$ $16q^2$ is a perfect square, as it is $(4q)^2$ . $\newline$ $9$ is a perfect square, as it is $3^2$ . $\newline$ The middle term, $24q$ , should be equal to $2 \times (4q) \times 3$ if the expression is a perfect square trinomial. $\newline$ Let's check: $2 \times (4q) \times 3 = 24q$ , which matches the middle term.
Factor as Perfect Square: Factor the expression as a perfect square trinomial. $\newline$ Since the expression fits the pattern of a perfect square trinomial, we can write it as: $\newline$ $(4q + 3)^2 = (4q)^2 + 2 \times (4q) \times 3 + 3^2$ $\newline$ This matches the original expression $16q^2 + 24q + 9$ .

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