Remainder and factor theorem

Front

What is the Remainder Theorem?

Back

The Remainder Theorem states that when a polynomial f(x) is divided by (x - c), the remainder is f(c).

Tags

CCSS.HSA.APR.B.2

Front

What is the Factor Theorem?

Back

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

Tags

CCSS.HSA.APR.B.2

Front

How do you determine if (x - 4) is a factor of f(x) = x³ + x² - 16x - 16?

Back

Evaluate f(4). If f(4) = 0, then (x - 4) is a factor.

Tags

CCSS.HSA.APR.B.2

Front

What is the remainder when a³ - 4 is divided by a + 2?

Back

The remainder is -12.

Tags

CCSS.HSA.APR.B.2

Front

Which binomial is a factor of f(x) = x³ - 6x² + 3x + 10?

Back

The factor is x + 1.

Tags

CCSS.HSA.APR.B.2

Front

What is a cubic polynomial?

Back

A cubic polynomial is a polynomial of degree three, which can be expressed in the form f(x) = ax³ + bx² + cx + d.

Front

What is an example of a cubic binomial?

Back

An example of a cubic binomial is x³ + 5.

Front

How can you find the factors of a polynomial?

Back

You can find the factors by using synthetic division, factoring by grouping, or applying the Factor Theorem.

Tags

CCSS.HSA.APR.B.2

Front

What does it mean if a polynomial has a remainder of 0 when divided by a binomial?

Back

It means that the binomial is a factor of the polynomial.

Tags

CCSS.HSA.APR.B.2

Front

What is synthetic division?

Back

Synthetic division is a simplified method of dividing a polynomial by a linear binomial of the form (x - c).

Tags

CCSS.HSA.APR.D.6