Question

Factor the expression completely over the complex numbers.

y^4+14y^2+49

Answer 1

1. y^2x2 + 2 x y^2 x 7 + 7^2
2. ( y^2 )^2 + 2 x 7 + 7^2
3. (y^2 + 7)^2

Answer 2

Thats not right

Answer 3

sorry this took so long

(y^2 + 7)^2 = 0

taking the square root of both sides

y^2 + 7 = 0

y^2 = -7

y = +/- i * sqrt(7)

so we can re-write y^2 + 7 = 0 as

(y + i *sqrt(7))(y - i * sqrt(7))

going back to the original polynomial, (y^2 + 7)^2 is just the square of the previous result, so simply square both factors

(y + i *sqrt(7))^2 * (y - i * sqrt(7))^2

= (y + i *sqrt(7))*(y + i *sqrt(7))*(y - i *sqrt(7))*(y - i *sqrt(7))