Download Algebra 3

Algebra 3
Review I 4.1 – 4.5
Name
Date
Per.
Answer the following. Be sure to use any methods that are specified in the directions and
to show enough work so that I can reproduce your results if necessary.
1. Write a polynomial equation of least degree with roots -4, 1, i, and –i.
2. State the number of complex roots for the equation x 3 + 2x 2 – 15x = 0. Then find the roots by
factoring the equation. (hint: look for a gcf first)
2. number of roots:____________
roots:_______________________
3. Solve the following by completing the square.
a) x 2 + 10x + 35 = 0
b) 4x 2 + 11x + 7 = 0
4. Find the discriminant of each equation and describe the nature of the roots. Then solve using
the quadratic formula.
a) 9x 2 – 12 x + 4 = 0
b) -x 2 – 10x – 7 = 0
5. Divide using synthetic division. Write your answer as Quotient +
c) 3x 2 + 2x = - 5
remainder
.
divisor
(2 x3  3x  5)  ( x  2)
6. Find the value of k so that the remainder of (x 3 + 3x 2 – kx – 24) ÷ (x + 4) is 0.
7. Is x + 2 a factor of x 3 + 3x 2 – 4? Explain why or why not.
8. Given that one zero is 3, find all of the zeros of x 3 – 6x 2 + 11x – 6.
9. Use Descartes’ Rule of Signs to determine the number of possible positive real zeros and the
number of possible negative real zeros for f(x) = x 5 + 2x 4 + 5x 3 + 6x 2 – 6x – 12.
+
–
10. Use Descartes’ Rule of Signs and the Rational Root Theorem to determine the number of
possible positive and negative real zeros and to list the possible rational roots of the following.
Then find the actual zeros. Be sure to show your work.
f(x) =
3x 3
–
4x 2
+
–
– 5x + 2
p
=
q
actual roots:_____________________
11. Approximate the real zeros of f(x) = x 4 – 3x 3 + 2x – 1 to the nearest tenth.
12. Approximate the real zeros of f(x) = x 3 – x + 1 to the nearest tenth.
Use the Upper Bound Theorem to find an integral upper bound and the Lower Bound
Theorem to find an integral lower bound of the zeros of each function.
13. f(x) = 2x 4 + 3x 3 – x 2 + x + 1
14. f(x) = x 3 + 3x 2 – 5x – 9