Question

Write the polynomial in a factored form
x^3 - 3x^2 - 10x

Answer 1

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

Explanation:

First, note that x is the common factor, then

`x^3-3x^2-10x=x(x^2-3x-10).`

Now find the discriminant of the quadratic polynomial
`x^2-3x-10:`

`D=(-3)^2-4\cdot (-10)=9+40=49.`

Thus,

`x_1=(-(-3)-√(49))/(2)=(3-7)/(2)=-2,\\ \\x_2=(-(-3)+√(49))/(2)=(3+7)/(2)=5.`

Hence,

`x^3-3x^2-10x=x(x^2-3x-10)=x(x+2)(x-5).`