Free Printable Analysis: Polynomials & Rationals

1.

State the possible rational zeros for the following function:

f\left(x\right)=3x^3-5x^2-11x-3

a)

$\pm1,\ \pm3,\ \pm\frac{1}{3}$

b)

$0,\pm1,\pm\frac{1}{3}$

c)

$\pm1,\pm3$

d)

$\pm1,\pm\frac{1}{3}$

2.

State the possible number of positive and negative zeros for the following function:

f\left(x\right)=8x^6-133x^3+125

a)

Positive Real Zeros: 1
Negative Real Zeros: 0

b)

Positive Real Zeros: 1
Negative Real Zeros: 1

c)

Positive Real Zeros: 2 or 0
Negative Real Zeros: 2

d)

Positive Real Zeros: 2 or 0
Negative Real Zeros: 0

3.

Using the Rational Root Theorem, find all rational zeros for the given function. Show your work.

f\left(x\right)=2x^3-21x^2-4x+7

a)

$\left\{\frac{1}{2}\right\}$

b)

$\left\{0\right\}$

c)

$\left\{\frac{1}{3}\right\}$

d)

$\left\{\frac{1}{4}\right\}$

4.

Using the Rational Root Theorem, find all rational zeros for the given function. Show your work.

f\left(x\right)=5x^3+29x^2+19x-5

a)

$\left\{\frac{1}{3},-\frac{5}{3},-1\right\}$

b)

$\left\{\frac{1}{5},-5,-1\right\}$

c)

$\left\{\frac{1}{5},-5,-2\right\}$

d)

$\left\{\frac{1}{5},-\frac{5}{3},-1\right\}$

5.

Determine between which consective integers one or more zeros of f(x) are located.

f\left(x\right)=x^3+x^2-5

a)

2 and 3

b)

-2 and -1

c)

-1 and 0

d)

1 and 2

6.

Approximate the real zeros of f(x) to the nearest tenth.

f\left(x\right)=x^3-5x^2+2

a)

$-0.5,\ 0.7,\ 4.9$

b)

$-0.6,\ 0.7,\ 4.9$

c)

$\pm\ 0.6$

d)

$-0.6,\ 0.7,\ 5.0$

7.

Solve the following rational equation. Show your work.

\frac{4}{3n^2}+\frac{1}{3n}=\frac{1}{n}

a)

$\left\{4\right\}$

b)

$\left\{-2\right\}$

c)

$\left\{2\right\}$

d)

$\left\{-4\right\}$

8.

Solve the following rational equation. Show your work.

$\frac{1}{r}=\frac{7r-6}{r\left(r-1\right)}+\frac{4}{r-1}$

a)

$\left\{2\right\}$

b)

$\left\{1\right\}$

c)

$\left\{-\frac{1}{2}\right\}$

d)

$\left\{\frac{1}{2}\right\}$

9.

Solve the following rational inequality. Show your work.

\frac{x+3}{x-8}<0

a)

$\left(-3,8\right)$

b)

$\left[-3,8\right)$

c)

$\left\{-3\right\}$

d)

$\left(-\infty,-3\right)U\left(8,\infty\right)$

10.

Solve the following rational inequality. Show your work.

$\frac{\left(x+6\right)\left(x+4\right)}{x-8}\ge0$

a)

$\left\{-6\right\}$

b)

$\left(-6,-4\right)U\left(8,\infty\right)$

c)

$\left[-6,-4\right]U\left(8,\infty\right)$

d)

$\left\{6\right\}$

Analysis: Polynomials & Rationals

Total questions: 10

Worksheet time: 30mins

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