Dividing Polynomials

Front

What is synthetic division?

Back

A method for dividing a polynomial by a linear divisor, which is faster and simpler than long division.

Front

What is the first step in synthetic division?

Back

Write the coefficients of the polynomial in descending order.

Front

How do you determine the number to place in the left-hand box during synthetic division?

Back

It is the zero of the linear divisor (x - c), where c is the value that makes the divisor equal to zero.

Front

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

Back

2x - 7.

Front

What is the order of polynomial coefficients in (3x - 4x^3 + 6x^4 + 1)?

Back

6, -4, 0, 3, 1.

Front

What is the quotient of 2x^3 - 5x^2 + 3x + 7 divided by x - 2?

Back

2x^2 - x + 1 + 9/(x - 2).

Front

When should you use synthetic division instead of long division?

Back

When dividing by a linear polynomial of the form (x - c).

Front

What is the remainder theorem?

Back

If a polynomial f(x) is divided by (x - c), the remainder is f(c).

Front

What is the relationship between the degree of the dividend and the divisor in polynomial division?

Back

The degree of the quotient is the degree of the dividend minus the degree of the divisor.

Front

What is the purpose of polynomial long division?

Back

To divide polynomials when synthetic division is not applicable.