Factor. 9z^2 + 24z + 16 ______

Identify Form: Identify the form of the quadratic trinomial. The given expression 9z^2 + 24z + 16 is a quadratic trinomial in the form of az^2 + bz + c.Rewrite a^2: Rewrite 9z^2 in the form of a^2. 3^2 = 9 9z^2 = (3z)^2Rewrite b^2: Rewrite 16 in the form of b^2. 4^2 = 16Identify a, b: Identify the values of a and b. Compare (3z)^2 with a^2 and 4^2 with b^2. a = 3z b = 4Check Middle Term: Check if the middle term 24z matches the form 2ab. 2 * (3z) * (4) = 24z The middle term matches the form 2ab, which suggests that the trinomial is a perfect square.Write Factored Form: Write the factored form of the expression 9z^2 + 24z + 16. a^2 + 2ab + b^2 = (a + b)^2 9z^2 + 24z + 16 = (3z + 4)^2 Factored form: (3z + 4)^2

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Algebra 2

Factor quadratics

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Q. Factor.

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9z^2 + 24z + 16

Identify Form: Identify the form of the quadratic trinomial. $\newline$ The given expression $9z^2 + 24z + 16$ is a quadratic trinomial in the form of $az^2 + bz + c$ .
Rewrite $a^2$ : Rewrite $9z^2$ in the form of $a^2$ . $\newline$ $3^2 = 9$ $\newline$ $9z^2 = (3z)^2$
Rewrite $b^2$ : Rewrite $16$ in the form of $b^2$ . $\newline$ $4^2 = 16$
Identify $a, b$ : Identify the values of $a$ and $b$ . Compare $(3z)^2$ with $a^2$ and $4^2$ with $b^2$ . $a = 3z$ $b = 4$
Check Middle Term: Check if the middle term $24z$ matches the form $2ab$ . $\newline$ $2 \times (3z) \times (4) = 24z$ $\newline$ The middle term matches the form $2ab$ , which suggests that the trinomial is a perfect square.
Write Factored Form: Write the factored form of the expression $9z^2 + 24z + 16$ . $\newline$ $a^2 + 2ab + b^2 = (a + b)^2$ $\newline$ $9z^2 + 24z + 16 = (3z + 4)^2$ $\newline$ Factored form: $(3z + 4)^2$