Factoring and Rational Expressions

The video tutorial explains how to divide rational expressions by converting the division into multiplication by the reciprocal. It covers the process of factoring trinomials, simplifying expressions by canceling common factors, and ensuring the final expression is in its simplest form. The tutorial provides step-by-step guidance on factoring complex trinomials and emphasizes the importance of checking the sum of inner and outer products to ensure correct factoring.

What is the first step in dividing rational expressions?

• Multiply the fractions directly

• Add the fractions

• Convert the division into multiplication by the reciprocal

• Convert the division into subtraction

What is the reciprocal of a fraction c/d?

• c-d

• 1/(c+d)

• d/c

• c/d

When factoring 6x^2 - 7x + 2, what method is used?

• Using the quadratic formula

• Grouping

• Trial and error

• Completing the square

In the expression 6x^2 - 7x + 2, what are the factors of 6x^2?

• 6x and x

• 3x and 2x

• Both A and B

• None of the above

What is the greatest common factor of 4x - 8?

• x

• 4

• 2

• 8

What is the result of factoring out the greatest common factor from 4x - 8?

• x + 2

• 2x - 4

• 4x - 2

• x - 2

Which pair of numbers are the factors of 6 that add up to -5 in the trinomial x^2 - 5x + 6?

• -6 and 1

• -3 and -2

• 6 and -1

• 3 and 2

What is the first step in factoring a trinomial?

• Find the product of the first and last terms

• Check for perfect squares

• Identify the leading coefficient

• Factor out the greatest common factor

What is the simplified form of the expression after canceling common factors?

• x - 2 over 1

• x - 3 over 2

• 3x - 2 over 4

• 2x - 1 over 3

Why can't the 2 and 4 in the final expression be simplified?

• They are not common factors

• They are part of addition or subtraction

• They are already in simplest form

• They are coefficients