Solve the equation by factoring: 3x^(3)-9x^(2)-12 x=0 Answer: x=

Factor GCF: Factor out the greatest common factor (GCF) from the equation. The GCF of 3x^3, -9x^2, and -12x is 3x. So we factor 3x out of each term. 3x(x^2 - 3x - 4) = 0Factor Quadratic: Factor the quadratic equation inside the parentheses. We need to find two numbers that multiply to -4 and add to -3. These numbers are -4 and +1. So the factored form of the quadratic is (x - 4)(x + 1). 3x(x - 4)(x + 1) = 0Solve for x (1): Set each factor equal to zero and solve for x. First, set 3x equal to zero: 3x = 0 x = 0Solve for x (2): Set the second factor equal to zero and solve for x. (x - 4) = 0 x = 4Solve for x (3): Set the third factor equal to zero and solve for x. (x + 1) = 0 x = -1

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Solve the equation by factoring:

3x^(3)-9x^(2)-12 x=0
Answer:
x=

Solve the equation by factoring: $\newline$ $3 x^{3}-9 x^{2}-12 x=0$ $\newline$ Answer: $x=$

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Algebra 2

Quadratic equation with complex roots

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Q. Solve the equation by factoring:

\newline

3 x^{3}-9 x^{2}-12 x=0

\newline

Answer:

x=

Factor GCF: Factor out the greatest common factor (GCF) from the equation. $\newline$ The GCF of $3x^3$ , $-9x^2$ , and $-12x$ is $3x$ . So we factor $3x$ out of each term. $\newline$ $3x(x^2 - 3x - 4) = 0$
Factor Quadratic: Factor the quadratic equation inside the parentheses. $\newline$ We need to find two numbers that multiply to $-4$ and add to $-3$ . These numbers are $-4$ and $+1$ . $\newline$ So the factored form of the quadratic is $(x - 4)(x + 1)$ . $\newline$ $3x(x - 4)(x + 1) = 0$
Solve for $x$ ( $1$ ): Set each factor equal to zero and solve for $x$ . $\newline$ First, set $3x$ equal to zero: $\newline$ $3x = 0$ $\newline$ $x = 0$
Solve for $x$ ( $2$ ): Set the second factor equal to zero and solve for $x$ . $(x - 4) = 0$ $x = 4$
Solve for $x$ ( $3$ ): Set the third factor equal to zero and solve for $x$ . $(x + 1) = 0$ $x = -1$