Question

y^3-6y+20 divided by y -3 ( find the answer by polynomial long division )

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Answer 1

Answer:

(y^2 -6y)^2 - 4(y^2 -6y + 3) - 20 = 0

Let y^2 -6y = x ——> 1

x^2 - 4(x + 3) - 20 = 0

x^2 - 4x - 12 - 20 = 0

x^2 - 4x - 32 = 0

x^2 - 8x + 4x - 32 = 0

x(x - 8) + 4(x - 8) = 0

(x + 4)(x - 8) = 0

x + 4 = 0, x - 8 = 0

x = -4, x = 8

Substitute x = -4 in equation 1,

y^2 -6y = -4

y^2 -6y + 4 = 0

y = (-(-6) +/- sqrt(36 - 16))/2

y = (6 +/- sqrt(20))/2

y = (6 +/- 2*sqrt(5))/2

y = 3 +/- sqrt(5)

y = 3 + sqrt(5), 3 - sqrt(5)

Substitute x = 8 in equation 1,

y^2 -6y = 8

y^2 -6y - 8 = 0

y = (-(-6) +/- sqrt(64 + 32))/2

y = (-(-6) +/- sqrt(96))/2

y = (-(-6) +/- 4*sqrt(6))/2

y = 3 +/- 2*sqrt(6)

y = 3 + 2*sqrt(6), 3 - 2*sqrt(6)

Therefore

y = 3 + sqrt(5), 3 - sqrt(5), 3 + 2*sqrt(6), 3 - 2*sqrt(6) ——> Answer

Step-by-step explanation:

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