Write each quadratic function below in terms of linear factors. a) f (x) = x²-25b) f (x) = x²+25c) f (x) = 4x²+25d) f (x) = x²-2x+1e) f (x) = x²-2x+4

a) (x + 5) (x - 5)

b) (x + 5i) (x - 5i)

c) (x + (5i/2)) (x - (5i/2))

d) (x-1) (x-1)

e) x + i√3 + 1) (x - i√3+1)

Step-by-step explanation:

To solve this, we will need to factorize each quadratic function making it equal to zero first and then proceeding to find x

a) f (x) = x²-25

x²-25 = 0

⇒ (x + 5) (x - 5)

b) f (x) = x²+25

x² + 25 = 0

x² = - 25

x = √-25

x = √25i

x = ±5i

⇒ (x + 5i) (x - 5i)

c) f (x) = 4x²+25

4x²+25 = 0

4x² = - 25

x² = - 25/4

x = ±√ (-25/4)

x = ± (√25i) / 2

x = ±5i / 2

⇒ (x + (5i/2)) (x - (5i/2))

d) f (x) = x²-2x+1

x²-2x+1 = 0

⇒ (x - 1) ²

e) f (x) = x²-2x+4

x²-2x+4 = 0

x²-2x = - 4

x²-2x + 1 = - 4 + 1

x²-2x + 1 = - 3

(x-1) ² + 3 = 0

(x-1) ² = - 3

x-1 = √-3

x = ±√3i + 1

⇒ (x + i√3 + 1) (x - i√3+1)