Factoring and Simplifying Expressions

The video tutorial covers simplifying rational expressions, focusing on finding undefined values and simplifying by factoring. It explains that undefined values occur when the denominator equals zero and demonstrates how to find these values through examples. The tutorial also covers simplifying expressions by canceling common terms in the numerator and denominator. Advanced techniques, such as factoring out negative ones, are discussed, with several example problems provided to reinforce learning.

What condition must be met for a rational expression to be undefined?

• The expression must be a whole number.

• The denominator must be zero.

• The numerator must be zero.

• The expression must be a fraction.

If Z + 5 is part of the denominator, what value of Z makes the expression undefined?

• Z = 1

• Z = -5

• Z = 0

• Z = 5

When factoring Y^2 - Y - 6, which pair of numbers is used to factor the expression?

• -1 and 6

• 3 and -2

• 1 and -6

• -3 and 2

What is the simplified form of the expression with a numerator of 4Y(Y - 3)(Y + 4) and a denominator of Y(Y - 3)(Y + 2)?

• 4(Y - 3)/(Y + 2)

• 4Y(Y - 3)/(Y + 4)

• 4(Y + 4)/(Y + 2)

• 4Y(Y + 4)/(Y + 2)

In the expression X^2 - 9, what technique is used to factor it?

• Difference of squares

• Sum of cubes

• Quadratic formula

• Completing the square

What is the result of simplifying the expression with a numerator of X - 3 and a denominator of X + 3?

• X - 3

• X + 3

• 1

• Cannot be simplified

How can you simplify an expression if the numerator and denominator have opposite signs?

• Add a constant to both

• Factor out a negative one

• Multiply by zero

• Divide by a constant

What is the simplified form of the expression with a numerator of X - 5 and a denominator of 2X + 1?

• X - 5

• 2X + 1

• (X - 5)/(2X + 1)

• Cannot be simplified

What is the value of X that makes the expression with a denominator of 3X undefined?

• X = 1

• X = 3

• X = -3

• X = 0

In the expression 2X - 7, what happens when you factor out a negative one?

• The expression becomes 2X - 7

• The expression becomes 2X + 7

• The expression becomes -2X + 7

• The expression becomes -2X - 7