Question

PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!! I CANNOT RETAKE THIS!!

Factor the expression completely over the complex numbers.

Answer 1

(x - 5i√2)(x +5i√2)

given the roots of a polynomial p(x), say x = a and x = b

then the factors are (x - a)(x - b)

and p(x) is the product of the factors ⇒ p(x) = (x - a)(x - b)

here x² + 50 = 0 ⇒ x² = - 50 → ( set = 0 for roots)

take the square root of both sides

x = ± √-50 = ± √(25 × 2 × -1) = √25 × √2 × √-1 = ± 5i√2

The roots are x = ± 5i√2

thus the factors are ( x - ( - 5i√2)) and (x - (+5i√2))

x² + 50 = (x + 5i√2)(x - 5i√2)