Question

3x³ − x² − 3x + 1

Answer 1

Let ${\displaystyle f\left(x\right)=3x^3-x^2-3x+1}$ be the given polynomial.

Now, putting  x = 1,we get

${\displaystyle f\left(1\right)=3{\left(1\right)}^3-{\left(1\right)}^2-3\left(1\right)+1}$

        ${\displaystyle =3-1-3+1=0}$

Therefore, (x-1)is a factor of polynomial f(x).

Now,

${\displaystyle f\left(x\right)=3x^2(x-1)+2x(x-1)-1(x-1)}$

        ${\displaystyle =(x-1)\{3x^2+2x-1\}}$

        ${\displaystyle =(x-1)\{3x^2+2x-1\}}$

        ${\displaystyle =(x-1)(x+1)(3x-1)}$

Hence (x -1),(x+1) and (3x - 1 )are the factors of polynomial f(x).