Factoring and Simplifying Expressions

The video tutorial explains how to divide rational expressions by converting the division into multiplication using the reciprocal of the divisor. It demonstrates the process of simplifying the expressions by factoring out common factors in the numerators and denominators. Two examples are provided: the first involves monomials, and the second involves binomials, illustrating the steps of factoring and simplifying to achieve the final quotient in simplest form.

What is the first step in dividing rational expressions?

• Add the numerators

• Multiply by the reciprocal

• Subtract the denominators

• Divide the coefficients

When simplifying rational expressions, what should you do with common factors?

• Multiply them

• Add them together

• Cancel them out

• Ignore them

What is the prime factorization of 9?

• 2 x 4

• 6 x 1

• 3 x 3

• 5 x 2

How do you write 12x^4 in terms of its prime factors?

• 2 x 2 x 3 x x

• 2 x 2 x 3 x x x x

• 3 x 3 x x x x

• 2 x 3 x 3 x x

What is the final simplified form of the expression in the first example?

• 3y^2 / 2x

• 4x^2 / 9y^3

• 9y^3 / 4x^2

• 2x / 3y^2

In the second example, what is the greatest common factor of 6x and 54?

• 3

• 6

• 12

• 9

What is the result of factoring 5x + 10?

• 5(x + 2)

• 5(x + 10)

• 5(x + 5)

• 10(x + 1)

What is the final quotient in the second example?

• 5/6

• 6/5

• 1/2

• 2/1

What should you do if a binomial does not factor further?

• Divide by a constant

• Add a term

• Leave it as is

• Multiply by a constant

What is the first step in factoring a polynomial?

• Factor out the greatest common factor

• Multiply all terms

• Divide by the smallest term

• Add all terms