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-√(3))(x+√(3))=0

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-√(3))(x+√(3))=0`

Answer 1

A) (x +2)(x -3)² = 0

Explanation:

Synthetic division by (x-3) gives the quadratic x² -x -6, which has factors (x -3) and (x +2). This is confirmed by another round of synthetic division.

The resulting factorization is ...

... (x +2)(x -3)² = 0

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A graph confirms a double zero at x=3 and one at x=-2.