Question

To be answered with full method

Can the following expression

${x}^{2} - 2 \: \sqrt[]{2} x - 30$
be factorised ? why ? If yes, write the method.

Answer this as per class 9 , Polynomials

Answer 1

HELLO DEAR,

${x}^{2} - 5 \sqrt{2}x + 3 \sqrt{2} x- 30 \\ \\ = > x(x - 5 \sqrt{2} ) - 3 \sqrt{2} (x - 5 \sqrt{2} ) \\ \\ = > (x - 3 \sqrt{2} )(x - 5 \sqrt{2} ) \\ \\ = > x = 3 \sqrt{2 } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: or \: \: \: \: \: \\ \\ \\ \: \: \: \: \: \: \: \: \: \: \: x = 5\sqrt{2}$

it can be factorise by this two no.

5√2 and 3√2

we know that:-

factorisation method

splitation of middle term = multiplication of first and Last term

here,

multiplication of first and last Term = -30

and middle term = -2√2
it can also be written as, [5√2-(3√2)]=2√2

and multiply of this no. = 15×2 =-30

hence it can be factorise

I HOPE ITS HELP YOU DEAR,
THANKS

Answer 2

Yes, The following polynomial can be factorised .

It can be factorised by splitting the middle term.

=x²-2√2x-30
= x²-5√2x+3√2x-30
= x( x - 5√2) + 3√2 ( x - 5√2 )
= ( x - 5 √2 ) ( x +3√2 )

Hope helped!