Factor completely. -3x^(2)+6x+9=

Identify quadratic trinomial and coefficients: Identify the quadratic trinomial and its coefficients. The given quadratic trinomial is -3x^2 + 6x + 9, where the coefficients are -3 for x^2, 6 for x, and 9 as the constant term.Factor out greatest common factor: Factor out the greatest common factor (GCF) from the trinomial. The GCF of -3x^2, 6x, and 9 is 3. However, since the leading coefficient is negative, we will factor out -3 to keep the squared term positive in the resulting trinomial. Factoring out -3 gives us: -3(x^2 - 2x - 3).Factor trinomial inside parentheses: Factor the trinomial inside the parentheses. We need to find two numbers that multiply to give -3 (the constant term) and add to give -2 (the coefficient of x). The numbers that satisfy these conditions are -3 and +1. Therefore, we can write the trinomial as: -3((x - 3)(x + 1)).Write final factored form: Write the final factored form. The factored form of the quadratic expression is: -3(x - 3)(x + 1).

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Factor quadratics

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Q. Factor completely.

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-3x^{2}+6x+9=

Identify quadratic trinomial and coefficients: Identify the quadratic trinomial and its coefficients. $\newline$ The given quadratic trinomial is $-3x^2 + 6x + 9$ , where the coefficients are $-3$ for $x^2$ , $6$ for $x$ , and $9$ as the constant term.
Factor out greatest common factor: Factor out the greatest common factor (GCF) from the trinomial. $\newline$ The GCF of $-3x^2$ , $6x$ , and $9$ is $3$ . However, since the leading coefficient is negative, we will factor out $-3$ to keep the squared term positive in the resulting trinomial. $\newline$ Factoring out $-3$ gives us: $-3(x^2 - 2x - 3)$ .
Factor trinomial inside parentheses: Factor the trinomial inside the parentheses. $\newline$ We need to find two numbers that multiply to give $-3$ (the constant term) and add to give $-2$ (the coefficient of $x$ ). $\newline$ The numbers that satisfy these conditions are $-3$ and $+1$ . $\newline$ Therefore, we can write the trinomial as: $-3((x - 3)(x + 1))$ .
Write final factored form: Write the final factored form. $\newline$ The factored form of the quadratic expression is: $-3(x - 3)(x + 1)$ .