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This printable supports Common Core Mathematics Standard HSA-APR.B.2

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## Remainder Theorem

1.
What is the remainder of $3x^2+x-6$ divided by $x-1$?
1. $-2$
2. $x-4$
3. $-4$
4. $-6$
2.
Which of the following are factors of the polynomial $p(x) = 2x^4-x^3-17x^2+25x-6 ?$ There may be more than one answer.
1. $2x-3$
2. $x-5$
3. $3x-4$
4. $x-2$
3.
For polynomial $f(x)$, if $f(0)=0$, which of the following MUST be a factor of $f(x) ?$
1. $x$
2. $x-4$
3. $x-1$
4. $x+1$
4.
Given polynomial $p(x)$, such that $p(3) = 23$, what is a possible answer for $p(x)$ divided by $x-3 ?$
1. $3x + 3 + 2/(x-3)$
2. $4x^2 - 3x + 1 + 23/(x-3)$
3. $23x^2 + x$
4. $x + 23$
5.
Given polynomial $q(x)$, such that $q(4)=0$, what is a possible answer for $q(x)$ divided by $x-4 ?$
1. $3x^2 + 3 - 4/(x-4)$
2. $x-10$
3. $x^2 + 1 + 2/(x-4)$
4. $x + 2 - 4/(x-4)$
6.
For polynomials $p(x)$ and $q(x)$, where $(p(x))/(x-1) = q(x) + b/(x-1)$, what value(s) of $b$ ensure that $p(1) = 0 ?$ There may be more than one correct answer.
1. $x-1$
2. $1$
3. $0$
4. Any real number
7.
For polynomials $f(x)$ and $g(x)$, where $(f(x))/(x-3) = g(x) + c/(x-3)$, what value(s) of c ensure that $f(3)!=0 ?$ There may be more than one correct answer.
1. 3
2. 0
3. 1
4. -3
8.
Given that $x+3$ is factor of polynomial $p(x) = ax^3+53x^2+46x-15$, what is the value of $a ?$
1. $200/9$
2. $-3$
3. $"Not enough information"$
4. $12$
9.
If $x-2$ is a factor of polynomial $p(x) = 8x^4 + 6x^3 - ax^2 - 13x + 30$, what is the value of $a ?$
1. Not enough information
2. 34
3. 45
4. 180
10.
Given polynomial $p(x) = ax^3 - 5x^2 + bx + 4$, where $x-2$ is a factor of $p(x)$, and where $(p(x))/(x+3) = q(x) - 110/(x+3)$, $q(x)$ being the quotient of $p(x)$ divided by $x+3$, what are the values of $a$ and $b ?$
1. $a = 2, b=-3$
2. $a=-15, b=68$
3. $a=3, b=-4$
4. $a=-31/5, b=164/5$
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