Pre-Calculus Flashcard Remainder and Factor Theorems

Front

What is the Remainder Theorem?

Back

The Remainder Theorem states that if a polynomial f(x) is divided by (x - c), the remainder of this division 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 - c) is a factor of f(x)?

Back

To determine if (x - c) is a factor of f(x), evaluate f(c). If f(c) = 0, then (x - c) is a factor.

Tags

CCSS.HSA.APR.B.2

Front

What is synthetic division?

Back

Synthetic division is a simplified form of polynomial long division used to divide a polynomial by a linear factor of the form (x - c).

Tags

CCSS.HSA.APR.D.6

Front

What is the result of synthetic division of (3x^3 - 5x^2 - 4x + 1) by (x + 3)?

Back

The result is -113.

Tags

CCSS.HSA.APR.D.6

Front

If P(-4) = 0, what can be concluded about P(x)?

Back

x + 4 is a factor of P(x).

Tags

CCSS.HSA.APR.B.2

Front

What is the significance of the remainder in polynomial division?

Back

The remainder indicates what is left over after dividing a polynomial by another polynomial. It can provide insights into the roots of the polynomial.

Tags

CCSS.HSA.APR.B.2

Front

How do you find the remainder when dividing by (x + c)?

Back

To find the remainder when dividing by (x + c), evaluate the polynomial at -c.

Tags

CCSS.HSA.APR.B.2

Front

What does it mean if a polynomial has a root at x = c?

Back

If a polynomial has a root at x = c, it means that (x - c) is a factor of the polynomial.

Tags

CCSS.HSA.APR.B.2

Front

What is the relationship between factors and roots of a polynomial?

Back

The roots of a polynomial are the values of x that make the polynomial equal to zero, and each root corresponds to a factor of the form (x - root).

Tags

CCSS.HSF-IF.C.7C