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## Class 8 Maths Chapter 14 Exercise 14.4 Solution

 Class: 8 Mathematics Chapter: 14 Factorisation Exercise: 14.4 Videos and PDF Solution

### Class 8 Maths Chapter 14 Exercise 14.4 Solution in Videos

Class 8 Maths Chapter 14 Exercise 14.4 Solution
Class 8 Maths Chapter 14 Exercise 14.4 Explanation
##### Factorisation of Quadratic Trinomials

Formula: (x² + px + q)
For factorising (x² + px + q), we find two numbers a and b such that (a + b) = p and ab = q.
Then, x² + px + q = x² + (a + b) x + ab = x² + ax + bx + ab
= x (x + a) + b (x + a)
= (x + a) (x + b)

### Factorise: (i) x² + 8x + 15 (ii) x² + 15x + 56

We have: (i) x² + 8x + 15
We can write this expression as:
P = 3 + 5 and q = 3 x 5
= x² + (3 + 5) x + 3 x 5
= (x + 3) (x + 5)

(ii) x² + 15x + 56
We can write this expression as:
P = 7 + 8 and q = 7 x 8
= x² + (7 + 8) x + 7 x 8
= (x + 7) (x + 8)

Formula: ax2 + bx + c
Factorization Method: Split b into two parts whose sum = b and product = ac. Now, we proceed as above to factorise, as shown below.

### Factorise: 2x² + 9x + 10

The given expression is 2x² + 9x + 10
Find two numbers whose sum = 9 and product = (2 x 10) = 20.
So, 2x² + 9x + 10 = 2x² + 4x + 5x + 10
= 2x (x + 2) + 5 (x + 2)
= (x + 2) (2x + 5)

### What are the 3 methods that can be used to solve a quadratic equation?

There are three basic methods for solving quadratic equations: factoring, using the quadratic formula, and completing the square.

### How do you Factorise quadratics?

To factorise a quadratic we have to go from an expression such as x² − 2x − 15 to the linear factors (x − 5) (x + 3) which generate it when multiplied out.
We can split -2 as -5 + 3 and -5 x 3 = -15
So, we can write x² − 2x − 15 = x² − 5x + 3x − 15
Or, x (x – 5) + 3 (x – 5)
Or, (x – 5) (x + 3)

### What is the importance of factoring?

Factoring is an important process that helps us understand more about our equations. Through factoring, we rewrite our polynomials in a simpler form, and when we apply the principles of factoring to equations.        