Solve the equation by factoring: x^(3)-9x^(2)+18 x=0 Answer: x=

Factor GCF: Factor out the greatest common factor (GCF) from the equation x^3 - 9x^2 + 18x = 0. The GCF of x^3, -9x^2, and 18x is x. Factor out x from each term. x(x^2 - 9x + 18) = 0Factor Quadratic: Now we need to factor the quadratic equation x^2 - 9x + 18. Look for two numbers that multiply to 18 and add up to -9. These numbers are -3 and -6. So, the factored form of the quadratic is (x - 3)(x - 6). x(x - 3)(x - 6) = 0Solve for x: Set each factor equal to zero and solve for x. First factor: x = 0 Second factor: x - 3 = 0, so x = 3 Third factor: x - 6 = 0, so x = 6Write Roots: Write down all the roots of the equation. The roots are x = 0, x = 3, and x = 6.

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Solve the equation by factoring:

x^(3)-9x^(2)+18 x=0
Answer:
x=

Solve the equation by factoring: $\newline$ $x^{3}-9 x^{2}+18 x=0$ $\newline$ 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}-9 x^{2}+18 x=0

\newline

Answer:

x=

Factor GCF: Factor out the greatest common factor (GCF) from the equation $x^3 - 9x^2 + 18x = 0$ . The GCF of $x^3$ , $-9x^2$ , and $18x$ is $x$ . Factor out $x$ from each term. $x(x^2 - 9x + 18) = 0$
Factor Quadratic: Now we need to factor the quadratic equation $x^2 - 9x + 18$ . Look for two numbers that multiply to $18$ and add up to $-9$ . These numbers are $-3$ and $-6$ . So, the factored form of the quadratic is $(x - 3)(x - 6)$ . $x(x - 3)(x - 6) = 0$
Solve for x: Set each factor equal to zero and solve for x. $\newline$ First factor: $x = 0$ $\newline$ Second factor: $x - 3 = 0$ , so $x = 3$ $\newline$ Third factor: $x - 6 = 0$ , so $x = 6$
Write Roots: Write down all the roots of the equation. $\newline$ The roots are $x = 0$ , $x = 3$ , and $x = 6$ .