Factoring Expressions and Trinomials

The video tutorial explains how to factor expressions with fractional exponents. It covers three examples: factoring using the greatest common factor, factoring trinomials, and factoring perfect square trinomials. Each example is broken down step-by-step, demonstrating the process of identifying common factors, rewriting expressions, and verifying the factored form. The tutorial emphasizes understanding the properties of exponents and applying them to simplify and factor expressions correctly.

What is the first step in factoring expressions with fractional exponents?

• Multiply all terms by the smallest exponent

• Factor out the greatest common factor

• Divide each term by the largest coefficient

• Add the exponents together

In the expression 2x^(2/3) + 4x^(1/3), what is the greatest common factor?

• 2x^(2/3)

• x^(1/3)

• 2x^(1/3)

• 4x^(1/3)

How do you verify that an expression has been factored correctly?

• By multiplying the factors to see if they equal the original expression

• By dividing the expression by the factor

• By adding the factors together

• By subtracting the factors from the original expression

What common denominator is used to factor the expression x^(2/5) - 7x^(1/5) - 18?

• 10

• 2

• 1

• 5

Which of the following is a factor of the expression x^(2/5) - 7x^(1/5) - 18?

• x^(1/5) + 9

• x^(1/5) - 2

• x^(1/5) + 2

• x^(1/5) - 9

What is the first step in factoring a perfect square trinomial?

• Check if the first and third terms are perfect squares

• Add the first and third terms

• Subtract the middle term from the first term

• Multiply all terms by 2

In the expression 9y^(1/2) + 30y^(1/4) + 25, what is the value of 'a' in the perfect square trinomial formula?

• 3y^(1/4)

• 30y^(1/4)

• 9y^(1/2)

• 5

What is the value of 'b' in the perfect square trinomial formula for the expression 9y^(1/2) + 30y^(1/4) + 25?

• 9y^(1/2)

• 3y^(1/4)

• 30y^(1/4)

• 5

How do you verify that an expression is a perfect square trinomial?

• By checking if 2ab equals the middle term

• By adding the first and last terms

• By dividing the middle term by 2

• By multiplying the first and last terms

What should you do after factoring a perfect square trinomial?

• Leave it as is

• Verify by multiplying the factors

• Add the factors together

• Subtract the factors from the original expression