Precalculus Mt 403
1. Use synthetic division to divide ! 2x
3
2.4-2.5 Review
−3x 2 +4x−7 and write your answer in fraction form.
x−2
2. What is the remainder when ! x 3 − 3x + 4 is divided by ! x + 2 ?
3. Use the Factor Theorem or synthetic division to determine whether ! x − 2 is a factor of
! x 9 − 512 . You must show your work and justify your conclusion.
4. Given ! x + 3 is a factor of ! f ( x ) = 5x 3 − 7x 2 − 49x + 51 , use synthetic division to help
completely factor ! f .
5. Use the Rational Zeros Theorem to write a list of all the potential rational zeros of
! r ( x ) = 4x 6 −17x 3 + 5 .
6. Find the exact values for all of the real zeros of the function ! g ( x ) = x 3 + 3x 2 − 3x − 9 . Name
the irrational zeros.
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7. Write a polynomial function in standard form for ! f ( x ) = 3( x − 2) x − 3i x + 3i . How
many x-intercepts does the graph of ! f have?
8. Write a polynomial function in factored form whose zeros include ! 3, − 4, and 2i . Don’t forget
to consider the Conjugate Roots Theorem. What is the constant term of this polynomial?
9. Write ! d ( x ) = x 3 − x 2 − x − 2 as the product of a linear and irreducible quadratic factors all with
real coefficients.
10. Find all of the complex zeros of ! f ( x ) = x 4 + x 3 − x 2 + 5x − 30 .