Hotmath Practice Problems

Title:
Hotmath Algebra 2
Author:
Hotmath Team
Chapter:Polynomial FunctionsSection:Rational Zeros and The Fundamental Theorem of Algebra

Problem: 1

If p/q is a rational number in lowest terms and if it is a zero of

f(x) = 10x4 + ax3 + bx2 + cx + 3, what is true about p and q? List the possible rational zeros of f.

Problem: 3

Obtain the possible rational zeros of the given polynomial, using the Rational –Zero Theorem.

P(x) = 8x3 + 2x2 + 4x +1

Problem: 5

Give all the possible rational zeros of f using the rational zero theorem:

f(x) = x4 + 3x2 – 36

Problem: 7

Give all the possible rational zeros of f using the rational zero theorem:

f(x) = 8x4 – 2x3 + x + 15

Problem: 9

Use the Rational–Zero Theorem to find rational zeros of g if g(x) = x3 – 9x.

Use an alternate technique to find the rational zeros of g.

Problem: 11

Tell whether the given x–value is a zero of the function.

f(x) = x3 – 3x2 + 9x – 27, x = 3i

Problem: 13

Use synthetic division to decide which of the factors 1, –1, 3 and –3 are zeros of the function:

f(x) = x3 + 5x2 – 9x – 45

Problem: 15

Use synthetic division to decide which of the factors 1, –1, 3 and –3 are zeros of the function:

f(x) = x4 + 4x3 + 4x2 – 4x – 5

Problem: 17

Choose a statement that is true about the given quantities:

A. The quantity in column A is greater.

B. The quantity in column B is greater.

C. The two quantities are equal.

D. The relationship cannot be determined from the given information.

Problem: 19

Solve the given equation. Identify whether the given equation has any multiple roots.

x2 – 12x + 36 = 0

Problem: 21

Find all the roots of the following equation by factoring and solving the resulting quadratic equations.

z4 – 16 = 0

Problem: 23

Determine all the real zeros of the function:

f(x) = x3 – 9x2 – 40x + 48

Problem: 25

Determine all the real zeros of the function:

f(x) = x3 – 9x2 + 8x + 60

Problem: 27

Determine all the zeros of the polynomial function.

f(x) = x4 + 4x3x2 – 16x – 12

Problem: 29

Determine all the zeros of the polynomial function.

f(x) = x3x2 + 81x – 81

Problem: 31

Determine all the zeros of the polynomial function.

f(x) = x4 + 8x3 + 16x2 + 32x + 48

Problem: 33

Write a polynomial function of least degree that has real coefficients, the given zeros, and a leading coefficient of 1.

3, 1, 5

Problem: 35

Write a polynomial function of least degree that has real coefficients, the given zeros, and a leading coefficient of 1.

–1, –3, –8

Problem: 37

Write a polynomial function of least degree that has real coefficients, the given zeros, and a leading coefficient of 1.

2i, –2i, 3

Problem: 39

Write a polynomial function of least degree that has real coefficients, the given zeros, and a leading coefficient of 1.

5, 5, 3 + i

Problem: 41

One of the zeroes of the function f(x) = x3 – 7x2 + 13x – 6 is at x = 2. Determine the other zeroes.

Problem: 43

One of the zeroes of the function f(x) = 3x3 + 5x2 + 4 is at x = –2. Determine the other zeroes.

Problem: 45

Given one zero of the polynomial function, determine the other zeros.

f(x) = x3 + 2x2 + x + 36, –4

Problem: 47

Choose any method to find all the real zeroes of f(x) = x4 – 5x2 – 7.