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

Answer:

A) (x +2)(x -3)² = 0

Step-by-step 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.