Solve the equation by factoring: x^(3)-3x^(2)-10 x=0 Answer: x=

Factor GCF: Factor out the greatest common factor (GCF) from the equation x^3 - 3x^2 - 10x = 0. The GCF of all terms is x, so we factor it out. x(x^2 - 3x - 10) = 0Factor Quadratic: Factor the quadratic equation x^2 - 3x - 10. We look for two numbers that multiply to -10 and add up to -3. These numbers are -5 and +2. So, the factored form of the quadratic is (x - 5)(x + 2). x(x - 5)(x + 2) = 0Solve for x: Set each factor equal to zero and solve for x. First factor: x = 0 Second factor: x - 5 = 0, which gives x = 5 Third factor: x + 2 = 0, which gives x = -2

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Solve the equation by factoring:

x^(3)-3x^(2)-10 x=0
Answer:
x=

Solve the equation by factoring: $\newline$ $x^{3}-3 x^{2}-10 x=0$ $\newline$ Answer: $x=$

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Algebra 2

Composition of linear and quadratic functions: find an equation

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Q. Solve the equation by factoring:

\newline

x^{3}-3 x^{2}-10 x=0

\newline

Answer:

x=

Factor GCF: Factor out the greatest common factor (GCF) from the equation $x^3 - 3x^2 - 10x = 0$ . The GCF of all terms is $x$ , so we factor it out. $x(x^2 - 3x - 10) = 0$
Factor Quadratic: Factor the quadratic equation $x^2 - 3x - 10$ . We look for two numbers that multiply to $-10$ and add up to $-3$ . These numbers are $-5$ and $+2$ . So, the factored form of the quadratic is $(x - 5)(x + 2)$ . $x(x - 5)(x + 2) = 0$
Solve for x: Set each factor equal to zero and solve for x. $\newline$ First factor: $x = 0$ $\newline$ Second factor: $x - 5 = 0$ , which gives $x = 5$ $\newline$ Third factor: $x + 2 = 0$ , which gives $x = -2$