write the polynomial in factored form x33x210x please show a

write the polynomial in factored form.
x^3-3x^2-10x
please show all the steps needed to solve the problem, thank you.

Solution

Dear Student

Thank you for using Chegg !!

Given

x^3 - 3x^2 - 10x

(x) (x^2 - 3x - 10)

For the given quadratic equation x^2 - 3x - 10 , clearly the sum of roots is 3 and product of roots is -10

Now for 10 there are only 3 factors 1,5,2

Now one of the factors shall be negative and the negative factor must be smalller than positive factor since sum is positive.

There the factors must be 5, -2

Therefore the equation can be written as

(x) (x^2 - 5x + 2x - 10)

(x) (x (x - 5) + 2(x-5))

(x) (x - 5) (x + 2)

Solution