Dividing polynomials

Front

What is polynomial division?

Back

Polynomial division is the process of dividing a polynomial by another polynomial, similar to long division with numbers. It can be done using long division or synthetic 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

What is the result of dividing 2x³ - 5x² + 3x + 7 by x - 2?

Back

2x² - x + 1 + 9/(x - 2)

Front

What is the result of dividing 2x³ + 4x² - 5 by x + 3 using synthetic division?

Back

2x² - 2x + 6 - 23/(x + 3)

Front

What is the missing term when dividing 2x³ + 5x² + 9 by x + 3?

Back

x

Front

In synthetic division, what does the left-hand box represent?

Back

The left-hand box represents the value of c in the divisor (x - c). For example, if dividing by (x - 2), the left-hand box would contain 2.

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) as it is quicker and simpler.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial. For example, in 2x³ - 5x² + 3x + 7, the degree is 3.

Front

What is a remainder in polynomial division?

Back

The remainder is what is left over after dividing one polynomial by another. It can be expressed as a fraction of the divisor.

Front

How do you check your work after polynomial division?

Back

You can check your work by multiplying the quotient by the divisor and adding the remainder. The result should equal the original polynomial.