Rational Root

Multiple Choice

Below are four possible zeros for this polynomial.

Figure out which one "works"

f(x) = x³ + 2x² - 11x - 12

• -3

• -4

• 1

• 6

Multiple Choice

Below are four possible zeros for this polynomial.

Figure out which one "works"

f(x) = x³ - 8x² - 23x + 30

• 3

• -1

• -10

• 1

Multiple Select

What is a rational number?

• Decimals that end

• Decimals that go on forever

• Fractions

• Negative Numbers

• Irrational Numbers

If rational numbers can be written as fractions, the irrational numbers cannot.

Rational numbers

• are ratios of two integers

• if you can convert a number into a fraction it is a rational number

• all positive and negative numbers

• decimals that terminate or have repeating patterns

Examples of Rational numbers

Multiple Select

Select all that are rational numbers

• 0.24

• -14.2

• $$2\ \frac{1}{5}$$

• $$-\frac{5}{6}$$

• $$0.\overline{3}$$

Multiple Select

Which of these are perfect squares?

• 14

• 16

• 9

• 53

• 2

Square Roots: perfect squares

Irrational Numbers

Multiple Choice

Which of the following is a COMPLETE  list of all possible Rational Zeros?
f(x) = x³ + 2x² - 6x + 8

• ±1, ±8

• ±1, ±2, ±4, ±8

• ±1, ±2, ±4

• 1, 2, 4, 8

​Rational Root Theorem

​If a polynomial has rational roots then the possible roots are:

Multiple Choice

According to the Rational Root Theorem, what are the all possible rational roots? 
2x³ - 11x² + 12x + 9 = 0

• ±1,±2

• ±1,±3,±9

• ±1,±3±9,±1/2,±3/2,±9/2

• ±1,±2,±1/3,±2/3,±1/9,±2/9

Multiple Choice

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

• ±1, ±7, ±1/3, ±7/3

• ±1, 7

• ±1, ±3, ±7, ±7/3

• ±1, ±3, ±7, ±1/3, ±7/3

Multiple Choice

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

• -1, 1, 3

• -1, 3/2, 3 

• -1/2, 3, 3

• -1/2, 1, 3

Multiple Choice

Solve by using Rational Root Theorem: 
x³ - 7x - 6 = 0

• 1, 2, 3

• -1, -2, - 3

• -1, -2, 3

• 1,-2,-3