Solve the equation by factoring: x^(3)-2x^(2)-48 x=0 Answer: x=

Factor GCF: Factor out the greatest common factor (GCF) from the equation x^3 - 2x^2 - 48x = 0. The GCF is x, so we factor it out to get x(x^2 - 2x - 48) = 0.Factor Quadratic: Factor the quadratic equation x^2 - 2x - 48. We look for two numbers that multiply to -48 and add up to -2. These numbers are -8 and +6. So, we can write the quadratic as (x - 8)(x + 6).Write Factored Form: Write the factored form of the original equation using the factors found in Step 2. The factored form is x(x - 8)(x + 6) = 0.Solve for x: Set each factor equal to zero and solve for x. First factor: x = 0 Second factor: x - 8 = 0, which gives x = 8 Third factor: x + 6 = 0, which gives x = -6Find Roots: Write down all the roots of the equation. The roots are x = 0, x = 8, and x = -6.

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Solve the equation by factoring:

x^(3)-2x^(2)-48 x=0
Answer:
x=

Solve the equation by factoring: $\newline$ $x^{3}-2 x^{2}-48 x=0$ $\newline$ Answer: $x=$

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Algebra 2

Quadratic equation with complex roots

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Q. Solve the equation by factoring:

\newline

x^{3}-2 x^{2}-48 x=0

\newline

Answer:

x=

Factor GCF: Factor out the greatest common factor (GCF) from the equation $x^3 - 2x^2 - 48x = 0$ . The GCF is $x$ , so we factor it out to get $x(x^2 - 2x - 48) = 0$ .
Factor Quadratic: Factor the quadratic equation $x^2 - 2x - 48$ . We look for two numbers that multiply to $-48$ and add up to $-2$ . These numbers are $-8$ and $+6$ . So, we can write the quadratic as $(x - 8)(x + 6)$ .
Write Factored Form: Write the factored form of the original equation using the factors found in Step $2$ . $\newline$ The factored form is $x(x - 8)(x + 6) = 0$ .
Solve for x: Set each factor equal to zero and solve for x. $\newline$ First factor: $x = 0$ $\newline$ Second factor: $x - 8 = 0$ , which gives $x = 8$ $\newline$ Third factor: $x + 6 = 0$ , which gives $x = -6$
Find Roots: Write down all the roots of the equation. $\newline$ The roots are $x = 0$ , $x = 8$ , and $x = -6$ .