Factoring Algebraic Expressions with Rational Exponents

This video tutorial covers the process of factoring algebraic expressions that contain rational exponents. It begins with an introduction to the concept and proceeds with several examples, each increasing in complexity. The tutorial explains how to identify and extract the greatest common factor, handle negative exponents, and apply advanced factoring techniques. By the end, viewers will have a comprehensive understanding of how to factor expressions with rational exponents.

What is the greatest common factor (GCF) of the coefficients 6, 12, and 9?

• 6

• 2

• 3

• 4

When factoring an expression, how do you determine the GCF of variables with rational exponents?

• Choose the variable with the lowest exponent

• Choose the variable with the middle exponent

• Choose the variable with the highest exponent

• Choose the variable with the exponent closest to zero

In the expression 8x^(4/5) - 6x^(2/5) - 2x^(1/5), what is the GCF of the coefficients?

• 3

• 2

• 4

• 1

How do you simplify the expression x^(4/3) / x^(1/3)?

• x^(1/3)

• x^(2/3)

• x^(3/3)

• x^(5/3)

What is the result of factoring the expression 45x^(-2/3) - 5x^(4/3)?

• 5x^(-2/3)(9 + x^2)

• 5x^(2/3)(9 - x^2)

• 5x^(2/3)(9 + x^2)

• 5x^(-2/3)(9 - x^2)

What is the square root of x^2 in the context of factoring a difference of squares?

• x^2

• x

• 2x

• x^1

In the expression 8(2x + 3)^(7/9) - 4(2x + 3)^(2/9), what is the GCF of the coefficients?

• 2

• 8

• 3

• 4

How do you handle negative exponents when factoring expressions?

• Ignore them

• Convert them to positive by moving terms

• Add them to the positive exponents

• Multiply them by -1

What is the GCF of the coefficients 15, 35, and 45?

• 9

• 7

• 5

• 3

In the expression 15(3x + 1)^(-2/5) + 35(3x + 1)^(3/5) - 45(3x + 1)^(-4/5), what is the lowest exponent?

• 3/5

• 2/5

• -2/5

• -4/5