Rational Root Theorem and Factor Theorem

Front

What is the Rational Root Theorem?

Back

The Rational Root Theorem states that any rational solution (or root) of a polynomial equation, in the form of p/q, must have p as a factor of the constant term and q as a factor of the leading coefficient.

Tags

CCSS.HSA.APR.B.2

Front

What is the Factor Theorem?

Back

The Factor Theorem states that a polynomial f(x) has a factor (x - c) if and only if f(c) = 0, meaning c is a root of the polynomial.

Tags

CCSS.HSA.APR.B.2

Front

How do you find possible rational roots using the Rational Root Theorem?

Back

List all factors of the constant term (p) and the leading coefficient (q). The possible rational roots are the ratios of these factors (p/q).

Tags

CCSS.HSA.APR.B.2

Front

Given f(x) = x^3 + 2x^2 - 11x - 12, find one rational root.

Back

The rational root is -4.

Tags

CCSS.HSA.APR.B.2

Front

List all possible rational roots for f(x) = x^3 + 2x^2 - 6x + 8.

Back

±1, ±2, ±4, ±8.

Front

What are the possible rational roots for 2x^3 - 11x^2 + 12x + 9 = 0?

Back

±1, ±3, ±9, ±1/2, ±3/2, ±9/2.

Front

List all possible rational zeros for p(x) = 3x^2 + x + 7.

Back

-1/3, -7/3, -1, -7, 1/3, 7/3, 1, 7.

Tags

CCSS.HSA.APR.B.2

Front

How do you verify if a number is a root of a polynomial?

Back

Substitute the number into the polynomial. If the result is zero, then it is a root.

Tags

CCSS.HSF-IF.C.7C

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables, coefficients, and exponents, combined using addition, subtraction, multiplication, and non-negative integer exponents.

Front

What is a zero of a polynomial?

Back

A zero of a polynomial is a value of x that makes the polynomial equal to zero.

Tags

CCSS.HSF-IF.C.7C