Question

ANSWER THE FOLLOWING
The area of a square 'A' is 25 cm2. The perimeter of square 'B' is 12
What is the area of square 'c'?
A
C С
B​

Answer 1

Step-by-step explanation:

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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).