How to Solve Polynomials — Step by Step Guide

Step-by-Step Method

1. 1

   Identify the degree of the polynomial: linear (1), quadratic (2), cubic (3).

2. 2

   A zero of a polynomial p(x) is a value of x for which p(x) = 0.

3. 3

   For a quadratic ax² + bx + c: sum of zeroes = -b/a, product of zeroes = c/a.

4. 4

   To factorise, use splitting the middle term or the factor theorem.

5. 5

   Factor theorem: if p(a) = 0, then (x - a) is a factor of p(x).

Worked Example

Common Mistakes to Avoid

• ✗

  Confusing the degree with the number of terms.

• ✗

  Forgetting that a polynomial can have zero, one, or multiple zeroes depending on its degree.

• ✗

  Errors in splitting the middle term — the two numbers must multiply to give a×c and add to give b.

• ✗

  Not verifying by multiplying the factors back together.

Practice Polynomials on SparkEd

Get free chapter-wise practice questions aligned to your board:

Frequently Asked Questions

How do I solve Polynomials problems?

Identify the degree of the polynomial: linear (1), quadratic (2), cubic (3). A zero of a polynomial p(x) is a value of x for which p(x) = 0.

What are common mistakes in Polynomials?

Confusing the degree with the number of terms. Forgetting that a polynomial can have zero, one, or multiple zeroes depending on its degree.

Which class covers Polynomials?

Polynomials is typically taught in Class 9, 10. SparkEd has free practice for all these grades.

Where can I practise Polynomials for free?

SparkEd offers free chapter-wise practice for Polynomials aligned to CBSE, ICSE, and IB curricula. Visit sparkedmaths.com to start.