Question

HELp I need to factor out : \[x ^{4} + 4x^{3} + 12x^{2} + 16x+16\] I

Answer 1

I got the answer but actually i do not know how to get there

Answer 2

\[x ^{4} + 4x^{3} + 12x^{2} + 16x+16\]

Answer 3

@quickstudent @mathmate @pooja195

Answer 4

@IrishBoy123

Answer 5

@inkyvoyd

Answer 6

Oh sorry, I don't exactly remember how to do this

Answer 7

:/

Answer 8

@Conqueror

Answer 9

any ideas ?

Answer 10

@whpalmer4

Answer 11

\[x^4+4x^3+12x^2+16x+16=x^2(x^2+4x+12+\frac{ 16 }{ x }+\frac{ 16 }{ x^2 })\]
\[=x^2\left\{ \left( x2+\frac{ 16 }{ x^2 } \right)+\left( 4x+\frac{ 16 }{ x } \right)+12 \right\} ...(1)\]
\[put~x+\frac{ 4 }{ x }=t\]
squaring
\[x^2+\frac{ 16 }{ x^2 }+8=t^2,x^2+\frac{ 16 }{ x^2 }=t^2-8\]
\[=x^2[(t^2-8)+4t+12]=x^2[t^2+4t+4]=x^2(t+2)^2\]
\[=x^2(x+\frac{ 4 }{ x }+2)^2=[x(x+\frac{ 4 }{ x }+2)]^2=(x^2+2x+4)^2\]

Answer 12

DUDE unbelievable!

Answer 13

really, thanks bro

Answer 14

yw