### Concept (1)

Long division can be used to divide a polynomial by another polynomial, in this case a binomial of lower degree. When **dividing polynomials**, we set up the problem the same way as any long division problem, but are careful of terms with zero coefficients. For example, in the polynomial x^3 + 3x + 1, x^2 has a coefficient of zero and needs to be included as x^3+ 0x^2+3x+1in the division problem.

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Sample Problems
(10)

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###### Problem 1

How to reduce fractions with square roots.

###### Problem 2

How to rationalize denominators using the conjugate.

###### Problem 3

How to rationalize denominators using the conjugate and reduce the result.

###### Problem 4

Dividing radicals with variables and integers that are not necessarily perfect squares.

###### Problem 5

Dividing radical monomials with integers and variables but no need to rationalize the denominator.

###### Problem 6

Dividing radical monomials with integers and variables by simplifying each first and then rationalizing the denominator.

###### Problem 7

Overview of rationalizing the denominator by simplifying the radical first or after the denominator has been rationalized.

###### Problem 8

Finding the square root of fractions whether either the numerator, denominator, or both are not perfect squares.

###### Problem 9

Dividing radical expressions with a binomial in the numerator and radical monomial in the denominator.

###### Problem 10

Multiplying by the conjugate to divide and simplify radical expressions with a radical binomial in the denominator.