Polynomial Division

Front

What is polynomial division?

Back

Polynomial division is the process of dividing a polynomial by another polynomial of equal or lower degree, similar to long division with numbers.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial.

Front

What is a zero of a polynomial function?

Back

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

Front

How do you determine if k is a zero of f(x)?

Back

To determine if k is a zero of f(x), substitute k into the function and check if f(k) = 0.

Front

What is synthetic division?

Back

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

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).

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.

Front

Perform the division: -2x^2 + 4x + 48 ÷ (x + 4).

Back

The result is -2x + 12.

Front

Perform the division: (3x^3 + 5x - 1) ÷ (x + 1).

Back

The result is 3x^2 - 3x + 8 - 9/(x + 1).

Front

Perform the division: (2x^3 - 5x - 7) ÷ (x - 2).

Back

The result is 2x^2 + 4x + 3 - 1/(x - 2).