B+C A
= cosec
2
2
In AABC; prove that sec
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Maths > Polynomials > Factor Theorem
Polynomials
Factor Theorem
In this part, we will look at the Factor Theorem, which uses the remainder theorem and learn how to factorise polynomials. Further, we will be covering the splitting method and the factor theorem method.
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Questions
Factor Theorem
remainder and factor theorem
If p(x) is a polynomial of degree n > 1 and a is any real number, then
x – a is a factor of p(x), if p(a) = 0, and
p(a) = 0, if x – a is a factor of p(x).
Let’s look at an example to understand this theorem better.
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Factor Theorem
3 mins read
Browse more Topics under Polynomials
Polynomial and its Types
Value of Polynomial and Division Algorithm
Degree of Polynomial
Factorisation of Polynomials
Remainder Theorem
Zeroes of Polynomial
Geometrical Representation of Zeroes of a Polynomial
Example:
Examine whether x + 2 is a factor of x3 + 3x2 + 5x + 6.
Solution: To begin with, we know that the zero of the polynomial (x + 2) is –2. Let p(x) = x3 + 3x2 + 5x + 6
Then, p(–2) = (–2)3 + 3(–2)2 + 5(–2) + 6 = –8 + 12 – 10 + 6 = 0
According to the factor theorem, if p(a) = 0, then (x – a) is a factor of p(x). In this example, p(a) = p(- 2) = 0
Therefore, (x – a) = {x – (-2)} = (x + 2) is a factor of ‘x3 + 3x2 + 5x + 6’ or p(x).
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