# Sample quiz on factoring cubic and quartic polynomials Main home here.

1. Let $f(x)$ be a polynomial. If $f(a)=0$, which of the following is definitely true?
$x+a$ is a factor of $f(x)$
$x-a$ is a factor of $f(x)$
$x-2a$ is a factor of $f(x)$
$x+2a$ is a factor of $f(x)$
2. For what value of $k$ are both $x-1$ and $x+1$ factors of the cubic $x^3+kx$?
$k=1$
$k=2$
$k=-2$
$k=-1$
3. Is it always possible to factor every polynomial over the integers?
Yes, by using the factor theorem
Yes, by using the remainder theorem
No, it is never possible
No, it is sometimes impossible
4. In a bid to factor $x^3-2x^2+3x-12$, which of the following values of $x$ is NOT worth testing according to the integral root theorem?
$8$
$6$
$4$
$2$
5. Factorize $x^4-1$ completely
$(x-1)^4$
$(x+1)^2(x-1)^2$
$(x-1)(x+1)(x^2+1)$
$(x^2+1)(x-1)(x-1)$
6. Factorize $(x-1)^3-125$
$(x-6)(x^2+3x-21)$
$(x+6)(x^2+3x+21)$
$(x-6)(x^2+3x+21)$
$(x+6)(x^2-3x-21)$
7. Factorize $x^3-x^2-x+1$
$(x-1)^{2}(x+1)$
$(x+1)^{2}(x-1)$
$(x-1)^3$
$(x+1)^3$
8. Factorize $x^4-8x^2+16$
$(x-4)^{2}(x+4)^{2}$
$(x-2)^{2}(x+2)^{2}$
$(x-4)^{2}(x+1)^{2}$
$(x-1)^{2}(x+4)^{2}$
9. What is the value of $k$ for which $x+2$ is a factor of the quartic polynomial $x^4+2x^3-2x+k$?
$k=-28$
$k=-4$
$k=28$
$k=4$
10. Factorize $x^3-3x^2-4x+12$ completely
$(x^2-4)(x-3)$
$(x^2-4)(x+3)$
$(x-2)(x+2)(x+3)$
$(x+2)(x-2)(x-3)$