Factoring and Simplifying Expressions

This video tutorial focuses on multiplying and simplifying rational expressions. It provides step-by-step examples, demonstrating how to factor expressions, cancel terms, and identify excluded values. The tutorial covers techniques such as finding the greatest common factor, using the difference of squares, and factoring by grouping. It also explains how to identify points of discontinuity in rational expressions.

What is the first step in simplifying the expression 7x + 14 divided by x squared minus eight?

• Divide by x

• Add 10 to both terms

• Factor out the greatest common factor

• Multiply both terms by 2

When factoring the expression x squared plus three x minus ten, what are the two numbers that multiply to -10 and add to 3?

• 2 and 5

• 5 and -2

• -5 and 2

• 3 and -3

In the second example, what is the greatest common factor of 5x squared minus 15x?

• 15

• 5x

• x

• 5

What technique is used to factor the expression 3x squared minus 48?

• Quadratic formula

• Difference of squares

• Sum of cubes

• Completing the square

Which of the following is an excluded value for the expression 2x squared plus 11x plus 12?

• x = 5

• x = -3/2

• x = 4

• x = 0

Why is it important to identify excluded values in rational expressions?

• To find the maximum value

• To avoid division by zero

• To simplify the expression

• To determine the range

In the third example, what is the result of factoring x cubed minus eight?

• (x + 2)(x^2 + 2x + 4)

• (x - 2)(x^2 - 2x + 4)

• (x + 2)(x^2 - 2x + 4)

• (x - 2)(x^2 + 2x + 4)

What is the greatest common factor of the expression 4x cubed minus 20x squared?

• 20x^2

• 4x

• 4x^2

• 20x

Which expression is not factorable in the third example?

• x squared minus seven x plus ten

• x cubed minus eight

• x squared plus two x plus four

• 4x squared plus 3

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

• 3x squared plus 4 divided by 3

• 4x squared plus 3 divided by 3

• 3x squared plus 4 divided by 2

• 4x squared plus 3 divided by 2