Rational Root Theorem

What is the Fundamental Theorem of Algebra?

• The degree of the polynomial determines what the x value will be
• The degree of the polynomial tells us how many solutions the polynomial will have.
• The number of possible rational zeros
• States that a complex number and its conjugate are solutions

Tags

CCSS.HSN.CN.C.9

Name the Theorem
If P(x) is a polynomial with rational coefficients, then the irrational roots of P(x) = 0 occur in conjugate pairs.

• Binomial Theorem
• Factor Theorem
• Conjugate Root Theorem
• Rational Root Theorem

What is the Rational Root Theorem?

• The degree of the polynomial determines what the x value will be

• The degree of the polynomial tells us how many solutions the polynomial will have.

• Making a list of p/q will produce a list of possible rational zeros

• States that a complex number and its conjugate are solutions

Use the Rational Root Theorem to list the possible rational zeros.

• A
• B
• C
• D

Tags

CCSS.HSA.APR.B.2

Use the Rational Root Theorem to list the possible rational zeros.

• A
• B
• C
• D

Tags

CCSS.HSA.APR.B.2

Which of the following is a COMPLETE  list of all possible Rational Zeros?
f(x) = 2x³ + 5x² - 9x + 5

• ±1, ±5, ±1/2, ±5/2
• ±1, ±2, ±5, ±1/2, ±5/2
• ±1, ±5
• ±1, ±2, ±5, ±1/2, ±5/2, ±2/5

Tags

CCSS.HSA.APR.B.2

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

Tags

CCSS.HSA.APR.B.3

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

Below are four possible zeros for this polynomial.
Figure out which one "works" and can be used to find the others.
f(x) = x³ + 2x² - 11x - 12

• -3
• -4
• 1
• 6

Tags

CCSS.HSF-IF.C.7C

Below are four possible zeros for this polynomial.

Figure out which one "works" and can be used to find the others.

f(x) = x³ - 8x² - 23x + 30

• 3

• -1

• -10

• 1

Tags

CCSS.HSF-IF.C.7C