Polynomial Division: 2 methods

Front

What is polynomial division?

Back

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

Front

What are the two main methods of polynomial division?

Back

The two main methods of polynomial division are long division and synthetic division.

Front

How do you determine if (x - c) is a factor of a polynomial?

Back

You can determine if (x - c) is a factor of a polynomial by using the Remainder Theorem: if the polynomial evaluated at c is zero, then (x - c) is a factor.

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 synthetic division?

Back

Synthetic division is a simplified form of polynomial division that is used when dividing by a linear factor of the form (x - c).

Front

What is the first step in synthetic division?

Back

The first step in synthetic division is to write down the coefficients of the polynomial being divided.

Front

How do you perform synthetic division?

Back

To perform synthetic division, bring down the leading coefficient, multiply it by c, add it to the next coefficient, and repeat until all coefficients are processed.

Front

What is the result of dividing x^2 - 6x + 8 by x - 2?

Back

The result is x - 4.

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What is the quotient when dividing 2x^3 + 5x^2 + 9 by x + 3?

Back

The quotient is 2x^2 - x + 3.

Front

What is the quotient of (x^4 - 10x^3 + 35x^2 - 50x + 24) ÷ (x^2 - 3x + 2)?

Back

The quotient is x^2 - 7x + 12.