Free Printable Solving Polynomial using Rational Root Theorem

1.

List the potential rational zeros of the polynomial function. Do not find the zeros.

$f(x)=6x^4+4x^{3\ }-2x^2+2$

a)

$\pm\frac{1}{6},\pm\frac{1}{3},\pm\frac{1}{2},\pm\frac{2}{3},\pm1,\ \pm2$

b)

$\pm\frac{1}{6},\pm\frac{1}{3},\pm\frac{2}{3},\pm1,\ \pm2,\ \pm3$

c)

$\pm\frac{1}{6},\pm\frac{1}{3},\pm\frac{2}{3},\pm1,\ \pm2,\pm6$

d)

$\pm\frac{1}{2},\pm\frac{2}{3},\pm1,\ \pm2,\pm3,\pm6$

2.

Which of the following is a COMPLETE list of all possible Rational Zeros?
f(x) = 3x³ + 2x² - 6x + 7

a)

±1, ±7, ±1/3, ±7/3

b)

±1, 7

c)

±1, ±3, ±7, ±7/3

d)

±1, ±3, ±7, ±1/3, ±7/3

3.

List the potential rational zeros of the polynomial function. Do not find the zeros.

$f(x)=-2x^{3\ }+3x^2-4x+8$

a)

$\pm\frac{1}{8},\pm\frac{1}{4},\pm\frac{1}{2},\pm1,\ \pm2$

b)

$\pm\frac{1}{2},\pm1,\ \pm2,\ \pm4,\pm8$

c)

$\pm\frac{1}{4},\pm\frac{1}{8},\pm1,\ \pm2,\pm4$

d)

$\pm\frac{1}{2},\pm\frac{2}{3},\pm1,\ \pm2,\pm3,\pm6$

4.

Solve by using Rational Root Theorem:
2x³ - 11x² + 12x + 9 = 0

a)

-1, 1, 3

b)

-1, 3/2, 3

c)

-1/2, 3, 3

d)

-1/2, 1, 3

5.

Solve by using Rational Root Theorem:
x³ + 3x² - 6x - 8 = 0

a)

-4, -1, 2

b)

-4, -1, ±√2

c)

1, 2, 4

d)

4,-1,√2

6.

Solve by using Rational Root Theorem:
x⁴ - x³ + 2x² - 4x - 8 = 0

a)

-1, 2, ±2

b)

-1, 2, ±2i

c)

1, -2, 4

d)

1, 2, 2i

7.

What are the zeros of the polynomial?

g(x) = 2x⁴ + 23x³ +19x² - 116x - 60

a)

2,-3,-10,1/2

b)

2, 3,-10,-1/2

c)

2,-3,-10,-1/2

d)

-2,-3,10,-1/2

8.

Solve $x^4-3x^3+5x^2-x-10=0$

List all the possible rational zeros. Find all the zeros

4 lines

9.

Find the zeros of the function: $f\left(x\right)=x^3-8x^2-x^{ }+8$

a)

-8, -1, 1

b)

-1, 1, 8

c)

1, -2, -8

d)

1, 2, 8

10.

f(x) = (x - 3)² (x - 1)³ (x² - 4)

Find both the x and y intercepts. Graph the function. Lable the intercepts. Indicate if the graph crosses or touches at the zeros.

Solving Polynomial using Rational Root Theorem

Total questions: 10

Worksheet time: 1hrs 20mins

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