Solve the equation by factoring: x^(3)-11x^(2)+10 x=0 Answer: x=

Factor GCF: Factor out the greatest common factor (GCF) from the equation x^3 - 11x^2 + 10x = 0. The GCF of all terms is x, so we factor it out. x(x^2 - 11x + 10) = 0Factor Quadratic: Now we need to factor the quadratic equation x^2 - 11x + 10. We look for two numbers that multiply to 10 and add up to -11. These numbers are -10 and -1. So, the factored form of the quadratic is (x - 10)(x - 1).Write Fully Factored Form: Write the fully factored form of the original equation. x(x - 10)(x - 1) = 0Apply Zero-Product Property: Apply the zero-product property, which states that if a product of factors equals zero, then at least one of the factors must be zero. So, we set each factor equal to zero: x = 0 x - 10 = 0 x - 1 = 0Solve for Roots: Solve each equation for x to find the roots. x = 0 x - 10 = 0 => x = 10 x - 1 = 0 => x = 1

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Algebra 2

Quadratic equation with complex roots

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Q. Solve the equation by factoring:

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x^{3}-11 x^{2}+10 x=0

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Answer:

x=

Factor GCF: Factor out the greatest common factor (GCF) from the equation $x^3 - 11x^2 + 10x = 0$ . The GCF of all terms is $x$ , so we factor it out. $x(x^2 - 11x + 10) = 0$
Factor Quadratic: Now we need to factor the quadratic equation $x^2 - 11x + 10$ . We look for two numbers that multiply to $10$ and add up to $-11$ . These numbers are $-10$ and $-1$ . So, the factored form of the quadratic is $(x - 10)(x - 1)$ .
Write Fully Factored Form: Write the fully factored form of the original equation. $\newline$ $x(x - 10)(x - 1) = 0$
Apply Zero-Product Property: Apply the zero-product property, which states that if a product of factors equals zero, then at least one of the factors must be zero. $\newline$ So, we set each factor equal to zero: $\newline$ $x = 0$ $\newline$ $x - 10 = 0$ $\newline$ $x - 1 = 0$
Solve for Roots: Solve each equation for $x$ to find the roots. $x = 0$ $x - 10 = 0 \Rightarrow x = 10$ $x - 1 = 0 \Rightarrow x = 1$