Factor Theorem and Remainder Theorem Quiz

1. Which is a factor of $x^3-4x^2+x+6$?

• A. $(x+2)$
• B. $(x-1)$
• C. $(x+3)$
• D. $(x-2)$

2. $2x^3-3x^2+kx+2$ has a factor $(x-2)$. Find $k$.

• A. $-3$
• B. $3$
• C. $0$
• D. $-1$

3. $x^3+3x^2-4=(x-1)(x^2+ax+4)$. Find $a$.

• A. $3$
• B. $2$
• C. $4$
• D. $-4$

4. $(3x-2)$ is a factor of $f(x)$. Which value of $x$ gives $f(x)=0$?

• A. $x=-\frac23$
• B. $x=\frac23$
• C. $x=\frac32$
• D. $x=2$

5. $x^3+px^2-5x+6$ leaves remainder $4$ when divided by $(x-1)$. Find $p$.

• A. $4$
• B. $-2$
• C. $2$
• D. $1$