Question

What is the factor of4x²-36x+81

Answer 1

Question

What are the factors of 4x² -36x + 81 ?

Answer

Method 1 :-

$\sf 4x^2 -36x + 81$

$\sf = (2x)^2 - 2(2x)(9) +81$

By using the identity

$\sf (a+b)^2 = a^2+b^2+2ab$

$\sf 4x^2 -36x + 81 = (2x-9)(2x-9)$

Factors = (2x-9) and (2x-9)

Method 2

By using middle term splitting method :-

$\sf 4x^2 -36x + 81$

$\sf = 4x^2 - 18x-18x+81$

$\sf = 2x (2x - 9) -9(2x-9)$

$\sf = (2x-9)(2x-9)$

Factors of 4x² -36x + 81 = (2x-9) and (2x-9).

Answer 2

$\rm\blue{Question\:given:}$

What is the factor of $\rm{4x²-36x+81}$

$\rm\pink{Answer:}$

$\rm\implies{4x²-36x+81}$

$\rm\implies{4x²-(18x-18x)+81}$

$\rm\implies{4x²-18x-18x+81}$

$\rm\implies{2x(2x-9)-9(2x-9)}$

$\rm\implies{(2x-9)(2x-9)}$

$\rm\implies{(2x-9)²}$

$\sf\green{More\: information:}$

•Factorisation: In factorisation a number is written as a product of it's factors.

In the solution the factors of $\rm{81\:are\:=1,3,9,27\:and\:81}$

And, $\rm{81=1×3×9×27×81}$ is called Prime factorisation of 81.

Hope it's helpful!