Question

Which of the following is/are factors of $x^3+3x^2-x-3?$
(a) $x+1$ (b) $x-1$
(c) $x+3$

• A. Only (a)
• B. Only (b)
• C. Both (a) and (b)
• D. All (a), (b) and (c)

Answer 1

The correct option is D All (a), (b) and (c)

Factors of the given polynomial will divide the given polynomial, completely.
To check which of the given expressions are factors of the given polynomial, we need to check for which of $f(-1);f\left(1\right);f(-3)=0$
Now, $f(-1)={(-1)}^3+3{\left(1\right)}^2-(-1)-3=-1+3+1-3=0$
$f\left(1\right)={\left(1\right)}^3+3{\left(1\right)}^2-\left(1\right)-3=1+3-1-3=0$
$f(-3)={(-3)}^3+3{\left(3\right)}^2-(-3)-3=-27+27+3-3=0$
So, all of these expressions are factors of the given polynomial.