Factoring and Solving Quadratic Expressions

This video tutorial explains how to determine when a rational expression is undefined by identifying when the denominator equals zero. It covers three examples: solving by isolating variables, using binomial factors, and factoring quadratics. The tutorial emphasizes that division by zero is undefined and provides step-by-step solutions for each example.

Why is a rational expression undefined when the denominator is zero?

• Because division by zero is undefined.

• Because the expression becomes positive.

• Because the numerator is zero.

• Because the expression becomes negative.

In the first example, what value of x makes the expression undefined?

• x = 32

• x = 8

• x = 4

• x = -8

What is the first step in solving the equation 4x - 32 = 0?

• Add 32 to both sides

• Subtract 32 from both sides

• Multiply both sides by 4

• Divide both sides by 4

What is the greatest common factor in the expression 4x - 32?

• 4

• 16

• 2

• 8

In the second example, what values of x make the expression undefined?

• x = 4 and x = 10

• x = -4 and x = 10

• x = 4 and x = -10

• x = -4 and x = -10

What is the product of the binomial factors in the second example?

• (x - 10)(x + 4)

• (x + 10)(x - 4)

• (x + 10)(x + 4)

• (x - 10)(x - 4)

In the third example, what are the factors of the quadratic expression x^2 - 9x - 10?

• (x - 10)(x + 1)

• (x + 10)(x - 1)

• (x + 10)(x + 1)

• (x - 10)(x - 1)

What values of x make the quadratic expression x^2 - 9x - 10 undefined?

• x = 1 and x = 10

• x = -1 and x = -10

• x = 1 and x = -10

• x = -1 and x = 10

What is the first step in factoring the quadratic expression x^2 - 9x - 10?

• Find the greatest common factor

• Find the factors of -10 that add to -9

• Divide by x

• Add 10 to both sides

What is the value of x when x + 1 = 0?

• x = 10

• x = 0

• x = -1

• x = 1