Remainder — Algebra II, what it means and where it is taught
What is left when the divisor no longer fits. Always lower degree than the divisor.
Taught in Algebra II.
Where it is taught
What it rests on
Work through these first if this one does not settle.
- Divisor — The polynomial you are dividing by.
What uses it later
This idea is needed for:
- Remainder theorem — Dividing f(x) by x - a leaves remainder f(a).
Practise this idea
9 questions in the course bank use Remainder, in Dividing Polynomials & the Factor Theorem, Complex Numbers, Decimals & Long Division. The first 8 are below; the rest are in those units.
Problem 1
Find the remainder when f(x)=x2+3x-5 is divided by x-1.
Worked answer
-1
f(1)=1+3-5=-1
Problem 2
Find the remainder when f(x)=x3-2x+4 is divided by x-2.
Worked answer
8
f(2)=8-4+4=8
Problem 3
Divide x2+7x+12 by x+3.
Worked answer
x+4
x2 ÷ x = x
Multiply back and subtract to get 4x+12
4x ÷ x = 4, remainder 0
Problem 4
Divide 2x2+5x-3 by x+3.
Worked answer
2x-1
2x2 ÷ x = 2x
2x(x+3)=2x2+6x, subtract to get -x-3
-x ÷ x = -1, remainder 0
Problem 5
Is x-2 a factor of x3-3x2+4? Answer yes or no.
Worked answer
yes
f(2)=8-12+4=0
A zero remainder means yes
Problem 6
Divide x3-8 by x-2.
Worked answer
x^2+2x+4
Synthetic division with 2: 1, 2, 4, remainder 0
Problem 7
Find the remainder when 2x3-3x2+x-5 is divided by x+1.
Worked answer
-11
2(-1)-3(1)+(-1)-5
=-2-3-1-5=-11
Problem 8
Simplify i12.
Worked answer
1
12 ÷ 4 leaves remainder 0
i0 pattern value is 1