Question

factorise X square + 20 X - 69​

Answer 1

$\huge \bold{ Factorisation}$

We Could solve this problem by the process called Splitting The Middle Term.

So, let's get to know a little about this.

Suppose, there's an equation = 6x^2 + 19x + 10

Let's solve this using Splitting The Middle Term's Process.

So first, you should find the product of first and last term. In our equation, the first term is 6x^2 and the last term is 10.

The product of 6x^2 and 10 is 60x^2.

Next step is to find the multiples of 60x^2

One multiple is 15 × 4.

We should select the multiples such that when you add or subtract those multiples the given answer should be equal to the middle term given in the question.

Getting it?

Yea so, coming to the example :

60x^2 + 15x + 4x + 10.

Let's now take numbers common in the given example. You'll get -

3x ( 2x + 5 ) + 2 ( 2x + 5 )

(3x + 2) (2x + 5)

So that's the concept of Splitting The Middle Term.

Coming to your question :

x^2 + 20x - 69

Let's find the product of the first and last term. Its 69x^2

One of The multiple of 69x^2 = 23 × 3

x^2 + 23x - 3x - 69.

Let's take the common terms.

x ( x + 23 ) - 3 ( x + 23 )

( x + 23 ) ( x - 3 )

Answer : ( x + 23 ) ( x - 3 )