Part 3: CHOOSE 2 problems from this Part! Factor each and find all zeros

Question

1) f (x) = x 4 + 125x 2) f (x) = x 4 + 5x 3 + 4x 2 + 20x

3) f (x) = x 4 - x 3 - 2x 2 + 2x 4) f (x) = x 4 - 8x

Answer 1

x⁴ + 125x = x(x³ + 125) = x(x + 5)(x² - 5x + 25)

x⁴ + 5x³ + 4x² + 20x = x(x³ + 5x² + 4x + 20) = x(x + 5)(x² + 4)

x⁴ - x³ -2x² + 2x = x(x³ - x² -2x + 2) = x(x - 1)(x² -2)

x⁴ - 8x = x(x³ - 8) = x(x - 2)(x² + 2x + 4)

Answer 2

x^4 + 125x = x(x^3 + 125) = x(x+5)(x^2-5x+25)

x^4 + 5x^3 + 4x^2 + 20x =

x(x^3+5x^2+4x+20) -

x(x^2(x+5)+4(x+5) = x(x^2+4)(x+5)

x^4 - x^3 -2x^2 + 2x =

x(x^3 -x^2 - 2x + 2) =

x(x^2(x - 1) - 2(x - 1)) =

x(x^2-1)(x-1)

x^4 - 8x = x(x^3 - 8) = x(x - 2)(x^2 +2x + 4)