Question

Factor x^3-4x^2-3x+18=0 given that 3 is a zero.

A) (x+2)(x-3)^2=0
B) (x-2)(x-3)^2=0
C) (x-2)(x-3)(x+3)=0
D) (x+2)(x-\sqrt{3})(x+\sqrt{3})=0

Answer 1

B: (x + 2)(x - 3)^2

Explanation:

This is only going to have 3 roots. One of them is (x - 3)

D does not look right. So let's solve it using synthetic division.

3 || 1 - 4 -3 18

3 -3 -18

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1 -1 -6 0

So what you have is a quadratic

• x^2 - x - 6 = 0 which will factor
• (x - 3)(x + 2) = 0
• x - 3 = 0
• x = 3
• x + 2 =0
• x = - 2
• (x - 3)(x - 3)(x + 2 ) = 0

The answer is B