Practice Problems - Polynomials and Rational Functions
Not what you're looking for?
1. Explain how synthetic division may be used to find the factors/zeros of a polynomial function. Give an example of how this is accomplished.
Use synthetic division to find the function value.
1) f(x) = 2x4 + 4x3 + 2x2 + 3x + 8; find f(-2).
Write the quadratic function in the form y = a(x - h)2 + k.
2) y = x2 - 2x - 9
Find the product.
3) [x - (-6 + √13)][x - (-6 - √13)]
Use the leading coefficient test to determine whether y→∞ or y→-∞ as x→ -∞.
4) y = -5x3 + 4x2 + 6x - 7
For the given function, find all asymptotes of the type indicated (if there are any).
5) f(x) = (x-9)/(x^2- 4) vertical
Use the rational zero theorem to find all possible rational zeros for the polynomial function.
6) P(x) = 3x3 + 43x2 + 43x + 27
Solve the inequality. Give answer in interval notation.
7) (x + 2)(x - 1)(x - 10) > 0
Solve the inequality.
8) (x+21)/(x+3) <2
Discuss the symmetry of the graph of the polynomial function.
9) f(x) = x2 + 2x - 1
Solve the absolute value equation.
10) |x2 - 10| = 4
Solve the quadratic inequality by graphing an appropriate quadratic function.
11) x2 - 2x - 8 ≤ 0
Use the theorem on bounds to establish the best integral bounds for the roots of the equation.
12) 6x3 - 7x2 + 7x + 9 = 0
State the degree of the polynomial equation.
13) 4(x + 8)2(x - 8)3 = 0
Purchase this Solution
Solution Summary
All questions neatly solved showing the steps in detail. Graphs included.
Solution Preview
The solution file is attached.
1. Explain how synthetic division may be used to find the factors/zeros of a polynomial function. Give an example of how this is accomplished.
Let us use synthetic division to determine if the given set of numbers are zeros of the given polynomial
{-3, 2} f(x) = 3x^3 + 5x^2 - 6x + 18.
3 3 5 -6 18
-9 12 -18
3 4 6 0
Since the last number (remainder) is 0, x = -3 is a zero of f(x) = 0 x + 3 is a factor of f(x)
2 3 5 -6 18
6 22 32
3 11 16 50
Since the last number (remainder) is nonzero, x = 2 is not a zero of f(x) = 0 x - 2 is a not factor of f(x) ANSWERS:
Synthetic division has been illustrated.
Use synthetic division to find the function value.
1) f(x) = 2x4 + 4x3 + 2x2 + 3x + 8; find f(-2).
-2 2 4 2 3 8
-4 0 -4 2
2 0 2 -1 10
ANSWERS:
f(-2) = Remainder = 10
Write the quadratic function in the form y = a(x - h)2 + k.
2) y = x2 - 2x - 9
y = x^2 - 2x - 9
y = x^2 - 2x + 4 - 13
y = (x - 2)^2 - 13
This is of the form y = a(x - h)^2 + k, where
a = 1, h = 2, k = ...
Purchase this Solution
Free BrainMass Quizzes
Geometry - Real Life Application Problems
Understanding of how geometry applies to in real-world contexts
Probability Quiz
Some questions on probability
Exponential Expressions
In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.
Solving quadratic inequalities
This quiz test you on how well you are familiar with solving quadratic inequalities.
Graphs and Functions
This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.