Pre-Calculus
Review 4.5/4.6
Finding Zeros Review
Type 1: Given f(x) = 4x3 – 3x2 – 8x + 4 ; is x – 2 a factor?
Type 2: Given f(x) = 2x5 – x4 – x2 + 1 , find the possible zeros – do not find zeros
Type 3: Given y = x3 – 2x2 + x – 2, find zeros (grouping)
Type 4: Given y = x3 + 8x2 + 11x – 20 find zeros (synthetic division, factor depressed
polynomial)
Type 5: Given y = x3 – 8x2 + 17x – 6 find zeros (synthetic division, quadratic depressed
polynomial)
Type 6: Given y = x4 + x3 – 3x2 – x + 2 find zeros ( synthetic division, group depressed
polynimal)
Type 7: Given y = 4x4 – 15x3 – 8x2 + 15x + 4 find zeros (synthetic division twice)
Type 1: Given f(x) = 4x3 – 3x2 – 8x + 4 ;
is x – 2 a factor?
Type 2: Given f(x) = 2x5 – x4 – x2 + 1 , find the
possible zeros – do not find zeros
Type 3: Given y = x3 – 2x2 + x – 2, find zeros
Type 4: Given y = x3 + 8x2 + 11x – 20 find
zeros
Type 5: Given y = x3 – 8x2 + 17x – 6 find zeros
Type 6: Given y = x4 + x3 – 3x2 – x + 2 find
zeros
Type 7: Given y = 4x4 – 15x3 – 8x2 + 15x + 4
find zeros
Review Worksheet
Section 4.1 and 4.5
Pre-Calculus
Name: ___________________________ Date: _____________________ Period: ____
1. f(x) = 2 (x - 1)5
a. Identify the parent function
b. List 3 points from the parent
function and graph
c. Describe the shift
d. modify your points from b
and graph the new function.
2. Form a forth degree polynomial given:
zeros of 3 multiplicity 2, 4 multiplicity 1, and -1 multiplicity 1.
3. Given f(x) = 2 (x + 3)3(x - 2)4
a. List each real zero and it’s multiplicity.
Then, Determine whether the graph
touches or crosses the x-axis.
b. Find the power function
4. f(x) = x3(x + 2)
a. Find the x and y intercepts
c. State the power function
b. Does the graph cross or touch at each x - intercept
d. Make a general sketch of the graph below
5. Given f(x) = 8x3 – 3x2 + x + 4, determine if x – 1 is a factor.
6. Find all the potential zeros for f(x) = x3 – 3x2 – 6x + 8. DO NOT FIND ACTUAL ZEROS
Find the real zeros for the following polynomials
7. f(x) = 2x3 – x2 + 6x – 3
8. f(x) = x3 – 3x2 – 6x + 8
9. f(x) = 4x3 + 4x2 – 7x + 2
11. f(x) = x5 – x4 – 44x3 + 8x2 – 32x + 48
10. f(x) = x4 – 4x3 + 9x2 – 20x + 20