Dividing Polynomials

Front

What is polynomial long division?

Back

Polynomial long division is a method used to divide a polynomial by another polynomial of the same or lower degree, similar to numerical long division.

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). It is faster and requires less writing than long division.

Front

How do you find the quotient of (21x² - 52x + 32) ÷ (7x - 8)?

Back

The quotient is 3x - 4.

Front

What is the result of dividing (4x² - 24x + 35) by (2x - 5)?

Back

The result is 2x - 7.

Front

If the area of a rectangular pool table is x² + 14x + 40 and the length is x + 4, what is the width?

Back

The width is x + 10.

Front

What is the first step in polynomial long division?

Back

The first step is to divide the leading term of the dividend by the leading term of the divisor.

Front

What is the remainder theorem?

Back

The remainder theorem states that the remainder of the division of a polynomial f(x) by (x - c) is equal to f(c).

Front

When should you use synthetic division instead of long division?

Back

Use synthetic division when dividing by a linear polynomial of the form (x - c) for efficiency.

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 the leading coefficient of a polynomial?

Back

The leading coefficient is the coefficient of the term with the highest degree in the polynomial.