Question

The Factor y6+4y³-1 is

Answer 1

Answer:

( y³ + 2 + √5 ) ( y³ + 2 - √5 )

Step-by-step explanation:

To find----> Factor of ( y⁶ + 4 y³ - 1 )

Solution --->

y⁶ + 4 y³ - 1

We can write , y⁶ = ( y³ )²

=> ( y³ )² + 4 ( y³ ) - 1

Let y³ = p ,

Now , putting y³ = p

=> p² + 4 p - 1

To make it perfect square , adding and subtracting 4 , we get ,

=> ( p² + 4p + 4 ) - 1 - 4

=> ( p² + 4p + 4 ) - 5

We have an identity , as follows ,

( a + b )² = a² + b² + 2ab , applying it here , we get,

=> ( p + 2 )² - ( √5 )²

Now we have an identity, as follows,

( a² - b² ) = ( a + b ) ( a - b ) , applying it as follows,

=> ( p + 2 + √5 ) ( p + 2 - √5 )

Putting p = y³ , in it , we get,

=> ( y³ + 2 + √5 ) ( y³ + 2 - √5 )