3. Polynomials
3.05 Remainder and factor theorems
Interactive practice questions
Christa wants to test whether various linear expressions divide exactly into $P\left(x\right)$P(x), or whether they leave a remainder. For each linear expression below, state the value of $x$x that needs to be substituted into $P\left(x\right)$P(x) to find the remainder.
a
$x+3$x+3
b
$8-x$8−x
c
$5+4x$5+4x
d
$6-x$6−x
Easy
1min
Fill in the gap to make the statement true.
Easy
1min
If $P\left(x\right)=-2x^4+7x^3-3x^2-6x-5$P(x)=−2x4+7x3−3x2−6x−5 and $A\left(x\right)=x+2$A(x)=x+2. Use the remainder theorem to find the remainder when $P\left(x\right)$P(x) is divided by $A\left(x\right)$A(x).
Easy
3min
Using the remainder theorem, find the remainder when $P\left(x\right)=-4x^4+6x^3+4x^2-7x+7$P(x)=−4x4+6x3+4x2−7x+7 is divided by $A\left(x\right)=3x-1$A(x)=3x−1.
Easy
5min
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