Question

Factor the expression over the complex numbers.

x^2+18


Factor the expression over the complex numbers.

x^2+36


Factor the expression completely over the complex numbers.

x^4−625

Factor the expression completely over the complex numbers.

y^4+12y^2+36


Factor the expression completely over the complex numbers.

y^3+2y^2+16y+32

Answer 1

Answer:

divide the answers by the largest common factor

Step-by-step explanation: for number 1

you would divide both numbers by 2 (the greatest/largest common factor) and get x + 9 and that is your answer

Answer 2

1. (x-i3√2)(x+i3√2)

x² + 18 = 0

x² = -18

x = ±√(-18)

x = ±i3√2

(x-i3√2)(x+i3√2)=0

2. (x + 6i)(x - 6i)

x² - (6i)² = x² - (6²)(i²) = x² - 36i² = x² + 36

x² - (6i)² = (x + 6i)(x - 6i)

x² + 36 = (x + 6i)(x - 6i)

(x + 6i)(x - 6i)

3. x^4 - 625 = (x^2+25)(x+5)(x-5)

a^2-b^2 = (a+b)(a-b)

x^4 - 625 = (x^2+25)(x^2-25)

x^2-25 = (x+5)(x-5)

x^4 - 625 = (x^2+25)(x+5)(x-5)

4. y^4 + 12y^2 + 36 =

(4^2 + 6)^2 =

((y + √-6) (y - √-6))^2=

(y + i √6)^2(y - i √6)^2 =

(y^2 + 2i √ 6y - 6)(y^2 - 2i √6y - 6)

5. Y³ + 2y² + 16y + 32

Y² (y+2) + 16 (y+2)

(Y² + 16) (y+2)