Simplifying Rational Expressions and Exponents

This video tutorial teaches how to rewrite polynomial expressions by applying the rules of fractions. It covers simplifying fractions, dividing polynomials, and rewriting rational expressions using sums and differences. The tutorial also addresses complex rational expressions with remainders and explains negative exponents and reciprocals. By the end, viewers will understand how to simplify and rewrite various polynomial expressions.

What is a rational expression?

• A product of two variables

• A sum of two fractions

• A ratio of two polynomial expressions

• A ratio of two integers

How can 36x^6 divided by 6x^2 be simplified?

• 6x^2

• 6x^4

• 6x^3

• 6x

What is the result of simplifying 4 divided by (w + 4)?

• w/4

• 4/(w+4)

• 1/w

• 1/(w+4)

What is the simplified form of 15x^3 divided by 5x?

• 3x^2

• 3x

• 5x

• 5x^2

What is the result of simplifying 25x^2 divided by 5x?

• x

• 5x

• 5

• 5x^2

What is the simplified form of 10x divided by 5x?

• 5

• x

• 2

• 2x

How do you rewrite 2x^2 + 4x - 12 divided by 2x?

• x + 2 - 6/x

• x + 2 + 6/x

• x - 2 + 6/x

• x - 2 - 6/x

How can you verify the correctness of a rewritten rational expression?

• By adding the divisor

• By multiplying the quotient by the divisor

• By subtracting the divisor

• By dividing the quotient by the divisor

What does an exponent of -1 indicate in a rational expression?

• Multiplication by the reciprocal

• Division by the term

• Addition of the term

• Multiplication by the term

What is the result of rewriting a rational expression with a negative exponent?

• Multiplying by the reciprocal

• Dividing by the term

• Adding the term

• Multiplying by the term