Factoring four terms

Question

x3+4x2+x+4

(x3+4x2)+(x+4)

x2(x+4)+(x+4)

?

 

x+4 is the common factor but i'm not understanding how to factor out from here.

Answer 1

x^2(x+4)+1*(x+4)

 

Let u = x+4

 

(x^2)(u)+1*(u)

 

Factor out the u

 

u*(x^2 + 1)

 

(x+4)(x^2 + 1)

 

You can go farther if you allow imaginary numbers:

 

(x+4)(x^2 - (√(-1))^2)

 

(x+4)(x+i)(x-i)

 

 

Answer 2

HiCor,

 

x³+4x²+x+4=x²(x+4)+1(x+4)

 

                   =(x²+1)(x+4)

 

 

Answer 3

Hi Cor;

x³+4x²+x+4

For the FOIL...

FIRST must be (x²)(x)=x³

OUTER must be (x²)(4)=4x²

INNER must be (1)(x)=1x=x

LAST must be (1)(4)=4

(x²+1)(x+4)

(x³+4x²)+(x+4)

x³+4x²+x+4

same as above.

x²(x+4)+(x+4)

x³+4x²+x+4

same as above.