Solve the equation by factoring: x^(3)-12x^(2)+32 x=0 Answer: x=

Identify common factor: Identify the common factor in the equation x^3 - 12x^2 + 32x = 0. All terms have an x in common, so factor out x. x(x^2 - 12x + 32) = 0Factor quadratic equation: Now we have a quadratic equation to factor: x^2 - 12x + 32. We need to find two numbers that multiply to 32 and add up to -12. The numbers -4 and -8 satisfy these conditions. So, we can factor the quadratic as (x - 4)(x - 8). x(x - 4)(x - 8) = 0Solve for x: Set each factor equal to zero and solve for x. First factor: x = 0 Second factor: x - 4 = 0, so x = 4 Third factor: x - 8 = 0, so x = 8

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve the equation by factoring:

x^(3)-12x^(2)+32 x=0
Answer:
x=

Solve the equation by factoring: $\newline$ $x^{3}-12 x^{2}+32 x=0$ $\newline$ Answer: $x=$

View step-by-step help

Home

Math Problems

Precalculus

Operations with rational exponents

Full solution

Q. Solve the equation by factoring:

\newline

x^{3}-12 x^{2}+32 x=0

\newline

Answer:

x=

Identify common factor: Identify the common factor in the equation $x^3 - 12x^2 + 32x = 0$ . All terms have an $x$ in common, so factor out $x$ . $x(x^2 - 12x + 32) = 0$
Factor quadratic equation: Now we have a quadratic equation to factor: $x^2 - 12x + 32$ . We need to find two numbers that multiply to $32$ and add up to $-12$ . The numbers $-4$ and $-8$ satisfy these conditions. So, we can factor the quadratic as $(x - 4)(x - 8)$ . $x(x - 4)(x - 8) = 0$
Solve for x: Set each factor equal to zero and solve for x. $\newline$ First factor: $x = 0$ $\newline$ Second factor: $x - 4 = 0$ , so $x = 4$ $\newline$ Third factor: $x - 8 = 0$ , so $x = 8$