College Algebra Questions and Problems With Solutions sample 6 : Polynomials
College algebra questions and problems on multiplying, dividing and finding polynomials are presented. The solutions are at the bottom of the page.
Question 1
Find the product of the polynomials P(x) = 2x 2 - 3x and Q(x) = 3x 2 + x - 5
Question 2
Find the quotient and the remainder when polynomial P(x) = 2x 4 - x 3 -3x 2 + 7x - 13 is divided by Q(x) = x 2 - 4
Question 3
Find the fourth degree polynomial P(x) whose graph is shown below.
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Figure 1. graph of fourth degree polynomial, question 3
Question 4
Find the remainder if 4 x 200 + 5 x 95 - 4 x 21 + 2x - 6 is divided by x - 1
Question 5
Find the third degree polynomial with leading coefficient -2 and having zeros 1, -2 and 3.
Question 7
Find all zeros of the polynomial P(x) = 3x 4 + 26 x 3 + 74 x 2 + 74 x + 15 knowing that P(x) has two rational zeros.
Question 7
Polynomial P(x) = x 3 + x 2 + c x + d has x - 2 as a factor and when divided by x - 1, the remainder is equal to 3. Find the constant c and d.
Question 8
P(x) is an even fourth degree polynomial function such that P(-2) = 0, P(x + 3) has a zero at x = 4 and P(0) = -9. Find P(x).
Question 9
The polynomial P(x) = 2 x 4 + 3 x 3 - 16 x 2 - 17 x + 12 has zeros at x = 1/2 and x = -3. Find the other zeros.
Question 10
Factor the following polynomials:
a) f(x) = x 3 - x 2 - 4 x + 4
b) f(x) = 2 x 2 - x 3
c) f(x) = x 2 - 2 x 4
d) f(x) = -(x 2 - 2 x - 3) 2
e) f(x) = x 4 + 3 x 3 + 3 x 2 + x
Question 11
A polynomial of degree 4 has a negative leading coefficient and simple zeros (i.e. zeros of multiplicity 1) at x = 2, x = -2, x = 1 and x = - 1. Is the y intercept below the x axis or above the x axis?
Question 12
Match the function to the graph.
1) f(x) = (x + 1)(x - 1) 2(x + 2) 2
2) f(x) = -(x + 1)(x - 1) 4
3) f(x) = (x + 1)(x - 1) 3(x - 3)
4) f(x) = (x + 1) 2(x - 1) 3
Figure 2. graph of 4 functions , question 12 matching
Question 13
Give four different reasons why the graph below cannot possibly be the graph of p(x) = x 4 - x 2 + 1.
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Figure 3. graph polynomial , question 13
Question 14
The graph of polynomial f is shown below.
a) Is the degree of f even or odd?
b) Is the leading coefficient negative or positive?
c) Can you find the degree of f from the graph?Explain your answer.
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Figure 4. graph polynomial , question 14
Question 15
If the polynomial 3x3 + q x2 + p x + 7, where q and p are real numbers, is divided by x2 - 1, the remainder is 5x + 4. Find q and p.