Rational Expressions and Factorization

This video tutorial covers the multiplication and division of rational expressions, emphasizing the similarity to fraction operations. It explains the importance of simplifying expressions by factoring numerators and denominators before multiplying. The tutorial provides several examples, demonstrating the process of identifying common factors and simplifying products. It also introduces division by converting it into multiplication using reciprocals, followed by examples to illustrate the method. The video concludes with a complex example, reinforcing the concepts taught.

What is the first step in multiplying two rational expressions?

• Divide the numerators by the denominators

• Subtract the numerators from the denominators

• Multiply the numerators and denominators

• Add the numerators and denominators

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

• Multiply them

• Add them together

• Ignore them

• Cancel them out

In the example of multiplying two fractions, what is the prime factorization of 20?

• 2 x 10

• 4 x 5

• 2 x 2 x 5

• 5 x 4

What is the simplified form of the product when multiplying 5x^3y and 4y?

• 20x^3y^2

• 10x^3y^2

• 2x^3y^2

• 5x^3y^2

In the example of multiplying trinomials, what is the factorization of y^2 + 4y - 5?

• (y + 2)(y - 3)

• (y + 4)(y - 1)

• (y + 3)(y - 2)

• (y + 5)(y - 1)

Why can't you simplify the expression y - 5 over y + 5?

• Because they are already in simplest form

• Because they are not factors

• Because they are connected by addition or subtraction

• Because they are not like terms

What is the first step in dividing rational expressions?

• Subtract the expressions

• Add the expressions

• Divide the numerators

• Multiply by the reciprocal

In the division example, what is the factorization of x^2 - 1?

• (x + 1)(x + 1)

• (x + 2)(x - 2)

• (x - 1)(x - 1)

• (x + 1)(x - 1)

What is the result of factoring out a negative from -z^3 + 1?

• z^3 - 1

• -z^3 - 1

• -z^3 + 1

• z^3 + 1

What is the simplified form of the expression after multiplying z^4 by the reciprocal of z^2 - 1?

• z^2 / (z + 1)

• z^3 / (z - 1)

• z^2 / (z - 1)

• z^3 / (z + 1)