Hello, Alexia!

Here's part (1) . . .

Cubic function: .

1) Find the roots and confirm them by remainder theorem.

We want to solve: .

It is easier to factor without those fractions.

Factor out

Factor "by grouping": .

Take out the common factor: .

Difference of squares: .

Set each factor equal to zero and solve:

. .

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Check

If is a root of , then

. . . . . . . . . . . . . . .check!

. . . . . . . . . . . . . . .check!

. . . . . . . . . . . . . . .check!