Factor Theorem

We will discuss here about the basic concept of Factor Theorem.

If the polynomial p(x) is divided by x - α then by division algorithm,

P(x) = (x - α) q(x) + R,

        where q(x) is the quotient and R is the remainder which is a constant.

Putting x = α in P(x) = (x - α) q(x) + R, we get,

p(α) = (α - α) q(α) + R

⟹ p(α) = R.

If R = p(α) = 0, then

p(x) = (x - α) q(x) and so (x - α) is a factor of p(x).

x - α is a factor of p(x) if p(α) = 0, and if p(α) = 0 then p(x) has a factor x - α.


Example on Factor Theorem:

Prove that x + 5 is a factor of 2x\(^{2}\) + 7x - 15. Now, x + 5 = x – (-5) and

p(-5) = 2 (-5)\(^{2}\) + 7(-5) - 15

          = 50 - 35 - 15

          = 0.

So, x - (-5), i.e., x + 5 is a factor of 2x\(^{2}\) + 7x - 15

Corollary: ax + b is a factor of p(x) if p(-\(\frac{b}{a}\)) = 0, and if p (-\(\frac{b}{a}\)) = 0 then p(x) has a factor x - α.






● Factorization



















10th Grade Math

From Factor Theorem to HOME


New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.



Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



Share this page: What’s this?

Recent Articles

  1. Multiplication of a Number by a 3-Digit Number |3-Digit Multiplication

    Mar 28, 24 03:14 PM

    Multiplying by 3-Digit Number
    In multiplication of a number by a 3-digit number are explained here step by step. Consider the following examples on multiplication of a number by a 3-digit number: 1. Find the product of 36 × 137

    Read More

  2. Multiply a Number by a 2-Digit Number | Multiplying 2-Digit by 2-Digit

    Mar 27, 24 05:21 PM

    Multiply 2-Digit Numbers by a 2-Digit Numbers
    How to multiply a number by a 2-digit number? We shall revise here to multiply 2-digit and 3-digit numbers by a 2-digit number (multiplier) as well as learn another procedure for the multiplication of…

    Read More

  3. Multiplication by 1-digit Number | Multiplying 1-Digit by 4-Digit

    Mar 26, 24 04:14 PM

    Multiplication by 1-digit Number
    How to Multiply by a 1-Digit Number We will learn how to multiply any number by a one-digit number. Multiply 2154 and 4. Solution: Step I: Arrange the numbers vertically. Step II: First multiply the d…

    Read More

  4. Multiplying 3-Digit Number by 1-Digit Number | Three-Digit Multiplicat

    Mar 25, 24 05:36 PM

    Multiplying 3-Digit Number by 1-Digit Number
    Here we will learn multiplying 3-digit number by 1-digit number. In two different ways we will learn to multiply a two-digit number by a one-digit number. 1. Multiply 201 by 3 Step I: Arrange the numb…

    Read More

  5. Multiplying 2-Digit Number by 1-Digit Number | Multiply Two-Digit Numb

    Mar 25, 24 04:18 PM

    Multiplying 2-Digit Number by 1-Digit Number
    Here we will learn multiplying 2-digit number by 1-digit number. In two different ways we will learn to multiply a two-digit number by a one-digit number. Examples of multiplying 2-digit number by

    Read More