Question

Solve by Factoring x³-5x²=36x

Answer 1

The equation x³-5x²=36x is solved by factoring out x and then factoring the resultant quadratic equation, yielding solutions x = 0, x = 9, and x = -4.

Step-by-step explanation:

To solve by factoring the equation x³-5x²=36x, we first need to move all terms to one side of the equation to have a standard form for factoring. We get x³ - 5x² - 36x = 0. Observing that all terms contain an x-factor, we factor out an x:

• x(x² - 5x - 36) = 0

Now we look for two numbers that multiply to -36 and add up to -5. These numbers are -9 and +4. Thus, we can factor the quadratic to get:

• x(x - 9)(x + 4) = 0

The solutions to the equation are the values of x for which the product equals zero, which occurs when x = 0, x = 9, or x = -4. These are the values of x that solve the original equation.