Question

Sis In order to identify the zeros of the function, a student factored the cubic function ()=−−f of , open x close , equals , x cubed , minus 3 , x squared , minus 10 x as shown. Describe and correct the error the student made

Answer 1

f(x)=x(x-5)(x+2)

Explanation:

Since the steps of the factorization of the polynomial f(x) is not given, I will proceed to give the correct factorization of f(x).

f(x)=x³-3x²-10x

First, we factor out x since it is a common term.

f(x)=x(x²-3x-10)

Next, we factorize the quadratic expression x²-3x-10.

f(x)=x(x²-5x+2x-10)

f(x)=x(x(x-5)+2(x-5))

f(x)=x(x-5)(x+2)

The correct factorization of the polynomial f(x)=x³-3x²-10x is: f(x)=x(x-5)(x+2)