Question

Factor completely, then place the factors in the proper location on the grid.

x^2n + 10x^n + 16

Answer 1

`(x^n + 2)(x^n + 8)`

Explanation:

The polynomial
`x^(2n)+10x^n + 16` can be factored exactly the same as the polynomial
`x^2 + 10x + 16`. Here it factors into two numbers which multiply to 16 but add to 8. These factors are 8 and 2. So it factors into the expression (x+8)(x+2).

For the polynomial
`x^(2n)+10x^n + 16` it factors into the same factors except x ^n is used instead. The factors are
`(x^n + 2)(x^n + 8)`