Question

If ( x 3- ) is a factor of x 3 - 2x 2 - 9x + 18 , then find the other two factors.

Answer 1

Step-by-step explanation:

Factor by grouping:

(

x

3

−

2

x

2

)

+

(

−

9

x

+

18

)

Starting on the left we can factor out an

x

2

x

2

(

x

−

2

)

On the right we can then factor out a

−

9

−

9

(

x

−

2

)

Observe:

x

2

(

x

−

2

)

+

−

9

(

x

−

2

)

*Notice how we have two

x

−

2

. We can then simply rewrite the expression as follows.

(

x

2

−

9

)

(

x

−

2

)

*Note: all we did was combine

x

2

and

−

9

and wrote

(

x

−

2

)

as one term instead of two.

We're not done just yet. We can still factor

(

x

2

−

9

)

into

(

x

−

3

)

(

x

+

3

)

So a completely factored expression is then:

(

x

−

3

)

(

x

+

3

)

(

x

−

2

)

Answer 2

Answer:

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