 # Factorization Method Class 10th

## Introduction

In the Factorization Method, we factorize the quadratic equation and put each factor equal to zero and then find the values of x. These values of x are the solution of the quadratic equation and are called the roots of the quadratic equation.

This can be understood by the following examples.

### Examples

Example – 1) Find the roots of the quadratic equation x2 + 5x + 6 = 0 by factorization method.

Solution – given equation   x2 + 5x + 6 = 0

Step (1) Comparing the equation with the standard form ax2 + bx + c = 0

a = 1, b = 5, c = 6

We take      a⨯c = 1⨯6 = 6    and      b = 5

Step (2) Now we have to take two numeric values so that their sum should be equal to b i.e., 5 and their multiplication should be equal to a⨯c i.e., 6. So, we take the numbers 2 and 3.

Note – if it is difficult to find the two numeric values, we can factorize the term a⨯c and make pair to get it easily.

Step (3) Now check

2+3 = 5 and 2⨯3 = 6 (these values satisfy)

Step (4) Now, break the middle term of the equation x2 + 5x + 6 with the help of the above sum 2+3 = 5

x2 + (2+3)x + 6 = 0

x2 + 2x + 3x + 6 = 0

Step (5) Now take common terms out from the first two terms and last two terms.

x(x + 2) + 3(x+2) = 0

(x+2) is again a common term so,

(x+2) (x+3) = 0

Step (6) Now putting each factor equals to zero.

(x+2) = 0   and    (x+3) = 0

x = -2    and         x = -3 Ans.

Both the values of x are the solution of the given quadratic equation and are called the roots of this equation.

We can check our answer by putting the values of x in the given quadratic equation.

x2 + 5x + 6 = 0

at x = -2,

(-2)2 + 5(-2) + 6 = 0

4 – 10 + 6 = 0

– 6 + 6 = 0

0 = 0

LHS = RHS

at x = -3,

(-3)2 + 5(-3) + 6 = 0

9 – 15 + 6 = 0

– 6 + 6 = 0

0 = 0

LHS = RHS

At both the values, LHS = RHS it means our answer is correct.

Example – 2) Find the roots of the quadratic equation 2x2 – 5x + 3 = 0 by factorization method.

Solution – 2x2 – 5x + 3 = 0             Here, a⨯c = 2⨯3 = 6 and b = -5

2x2 – (2+3)x + 3 = 0                        two numeric values -2 and -3

2x2 – 2x – 3x + 3 = 0                       -2⨯(-3) = 6 and -2 + (-3) = -2 – 3 = -5

2x(x-1) -3(x-1) = 0

(x-1) (2x-3) = 0

(x-1) = 0   and   (2x-3) = 0

x = 1    and       x = 3/2

Thus, the roots of the quadratic equation 2x2 – 5x + 3 = 0 are x = 1 and x = 3/2.    Ans.

Factorization Method Class 10th in Hindi