Polynomials
Degree, values, zeroes and the remainder and factor theorems.
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A zero of a polynomial is where its graph crosses the x-axis.
Look: x² − 2x − 3 crosses the x-axis at −1 and 3. Those are its zeros.
✏️ Your turn!
Type your answer and press Check. Kutty will tell you if it is right.
1Zero of 2x − 6?
2Zeros of x² − 9?
3Factorise x² − 5x + 6.
! Careful!
✗Testing −2 to check (x − 2).
✓For (x − 2), test +2.
✗Degree of 3x⁴ + x⁵ is 4.
✓Degree is the biggest power: 5.
See the whole lesson on one page
A zero of a polynomial is where its graph crosses the x-axis.
A polynomial is like 2x³ − x + 5. Put a number in for x. If you get 0, that number is a zero, and (x − that number) is a factor.
Think of it like thisA ball’s height can be written as a polynomial. The zero tells you the moment it lands on the ground (height 0).
- Degree
- The biggest power: x² + 3 has degree 2.
Solved together
Is x = 2 a zero of x³ − 3x² − 4x + 12?
Put 2 in for x.
8 − 12 − 8 + 12Work it out.
= 0It gives 0, so 2 is a zero, and (x − 2) is a factor.
AnswerYes: x = 2 is a zero.
For older learners and grown-ups: a little more
Remainder theorem: dividing p(x) by (x − a) leaves remainder p(a). Here x³ − 3x² − 4x + 12 = (x − 2)(x + 2)(x − 3).
Now practise it
Kanakku makes new questions on polynomials every time. It shows the working and gives a hint when you are stuck.