Question

find the factors of the polynomial 4x²+y²+4xy+8x+4y+4

Answer 1

Step-by-step explanation:

(2x+y)²-4(2x+y) +3

..

let (2x+y)=a

a²-4a+3

a²-3a-a+3

a(a-3)-1(a-3)

(a-1)(a-3)

replace the value of a with 2x+y

(2x+y-1)(2x+y-3)

Answer 2

As per the data given in the above question.

We have to find the factor of given polynomial.

Given,

$4x²+y²+4xy+8x+4y+4$

Step-by-step explanation:

We have identity

$(a+b+c)²= \\ a²+ b²+ c²+2ab + 2bc + 2ca \: \: ..(1)$

The given polynomial has different terms , First arrange the terms , we get

$(2x)²+(y)²+(2)²+ 2(2x)(y) +2(y)(2) +2(2x)(2)\: \: \: \: ...(2)$

Now ,Compare the equation (1) and (2) we get

a= 2x

b= y

c= 2

So ,

$(2x+y+2)²= 4x²+y²+4 + 4xy+4y + 8x$

Hence ,

The factor of the given polynomial is

$(2x+y+2)²$

Project code #SPJ3