Question

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

Answer 1

Answer:

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

Step-by-step 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,

$x_1=\dfrac{-(-3)-\sqrt{49}}{2}=\dfrac{3-7}{2}=-2,\\ \\x_2=\dfrac{-(-3)+\sqrt{49}}{2}=\dfrac{3+7}{2}=5.$

Hence,

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