Question

x^2-2x+1 ————-Factorise

Answer 1

I hope this will help you

Answer 2

Factorisation :

$:\implies\bf{x^{2} - 2x + 1}$

Now,

Steps for Factorisation :-

• Multiple the coefficient of x² with the constant.

• Use Split Middle term Method :

• According to the Split Middle term Method - The middle term of the given expression will need to be split in such a way that their sum is equal to the middle term and their product is equal to the product of coefficient of x² and constant term.

• Now, taking common between two terms and making pair.

• Then, we will get our two factors.

Lets do the given question now :-

$:\implies\bf{x^{2} - 2x + 1}$

Now, As we see -

• Coefficient of x² = 1
• Constant Term = 1

And their L.C.M will also be " 1 "

Using Split Middle Term Method

$:\implies\bf{x^{2} - 2x + 1}$

$:\implies\sf{x^{2} - (1 + 1)x + 1}$

$:\implies\sf{x^{2} - 1x -1x + 1}$

Taking common :

$:\implies\sf{x(x - 1) -1(x - 1}$

$:\implies\bf{(x - 1) (x - 1)}$

Hence, (x - 1) and (x - 1) are the factors of polynomial p(x) = $\sf{x^{2} - 2x + 1}$

$\boxed{\therefore \sf{x = 1}}$

That's all we have to do in this question.

____________________________