Question

factorise x power 4+ 4x power 2 +16

Answer 1

 Best Answer

x⁴+ 4x² + 16 
= x⁴+ 16 + 4x² 

We need to make a perfect square, so we will add 8x² and - 8x² 
= ( x² )² + ( 4 )² + 2( x² )( 4 ) - 2( x² )( 4 ) + 4x² 

Make it a perfect square. 
= ( x² + 4 )² - 8x² + 4x² 
= ( x² + 4 )² - 4x² 

Write 4x² in the squared form 
= ( x² + 4 )² - ( 2x )² 

Now factorise by the formula of difference of 2 square a² - b² = ( a + b )( a - b ) 
= ( x² + 4 + 2x )( x² + 4 - 2x ) 

Arrange 
= ( x² + 2x + 4 )( x² - 2x + 4 ) 

Hope this helps .

Answer 2

Answer:

0

Step-by-step explanation:

x-2)x^4-3x^2+4(x^3+2x^2+x-2

+x^4-2x^3

- +

____________

2x^3-3x^2

+2x^3-4x^2

- +

______________

x^2+4

+x^2+2x

- -

_______________

-2x+4

-2x+4

+ -

____________

0

____________