Factor the four polynomial by grouping.

Question

x^3+8x^2+8x+64=?

(Factor completely.)

Answer 1

     x³ + 8x² + 8x + 64

When using grouping to factor a polynomial (usually with 4 or more terms), look at only two terms at a time to see if you can find a greatest common factor among each set of terms. 

For instance, look a the first two terms and the last two terms separately in the polynomial above and look for a gcf:

               x³ + 8x² + 8x + 64

   x³ + 8x²   ==>   gcf = x² , factor it out from both terms   ==>   x²(x + 8)

   8x + 64   ==>   gcf = 8 , factor it out from both terms   ==>   8(x + 8) 

              x³ + 8x² + 8x + 64

             x²(x + 8) + 8(x + 8)

Now we are left with two terms, one being the factored form of the first two terms (bold) and the other being the factored form of the last two terms (italics). Looking at the two terms that are left we see that they share a common factor, that being   'x + 8', that we can factor out of both terms.

             x²(x + 8) + 8(x + 8)   ==>   gcf = (x + 8) , factor it out of both terms

   ==>   (x + 8)(x² + 8)

Thus, 

          x³ + 8x² + 8x + 64 = (x² + 8)(x + 8)