Factor. 9g^2 + 6g + 1 ______

Check Pattern: Determine if the quadratic can be factored as a perfect square trinomial. A perfect square trinomial is in the form (ag + b)^2 = a^2g^2 + 2abg + b^2. We need to check if 9g^2 + 6g + 1 fits this pattern.Identify Terms: Identify the square root of the first term and the last term. The square root of 9g^2 is 3g, and the square root of 1 is 1. So, we have a = 3g and b = 1.Middle Term Check: Check if the middle term is twice the product of a and b. The middle term is 6g, and twice the product of 3g and 1 is 2 * 3g * 1 = 6g. Since the middle term matches, we can conclude that 9g^2 + 6g + 1 is a perfect square trinomial.Write Factored Form: Write the factored form using the square root of the first and last terms. The factored form is (3g + 1)^2.

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Algebra 1

Factor quadratics: special cases

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Q. Factor.

\newline

9g^2 + 6g + 1

Check Pattern: Determine if the quadratic can be factored as a perfect square trinomial. $\newline$ A perfect square trinomial is in the form $(ag + b)^2 = a^2g^2 + 2abg + b^2$ . $\newline$ We need to check if $9g^2 + 6g + 1$ fits this pattern.
Identify Terms: Identify the square root of the first term and the last term. $\newline$ The square root of $9g^2$ is $3g$ , and the square root of $1$ is $1$ . $\newline$ So, we have $a = 3g$ and $b = 1$ .
Middle Term Check: Check if the middle term is twice the product of $a$ and $b$ . The middle term is $6g$ , and twice the product of $3g$ and $1$ is $2 \times 3g \times 1 = 6g$ . Since the middle term matches, we can conclude that $9g^2 + 6g + 1$ is a perfect square trinomial.
Write Factored Form: Write the factored form using the square root of the first and last terms. $\newline$ The factored form is $(3g + 1)^2$ .