Sample quiz on factoring cubic and quartic polynomials
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- Let $f(x)$ be a polynomial. If $f(a)=0$, which of the following is definitely true?
- For what value of $k$ are both $x-1$ and $x+1$ factors of the cubic $x^3+kx$?
- Is it always possible to factor every polynomial over the integers?
- 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?
- Factorize $x^4-1$ completely
- Factorize $(x-1)^3-125$
- Factorize $x^3-x^2-x+1$
- Factorize $x^4-8x^2+16$
- What is the value of $k$ for which $x+2$ is a factor of the quartic polynomial $x^4+2x^3-2x+k$?
- Factorize $x^3-3x^2-4x+12$ completely