Factoring Quadratic Expressions

The video tutorial reviews the process of factoring quadratic expressions, starting with a simple example of x^2 + 4x - 5. It explains how to find two numbers whose product is -5 and sum is 4, leading to the factors (x - 1)(x + 5). The tutorial then introduces a more complex expression, x^2 + 4xy - 5y^2, involving two variables. It demonstrates how to apply the same factoring principles by considering terms with variables, resulting in the factors (x - y)(x + 5y). The video emphasizes understanding the structure of expressions and using consistent methods to factor them.

What is the first step in factoring a quadratic expression like x^2 + 4x - 5?

• Find two numbers whose sum is -5

• Find two numbers whose product is 5

• Find two numbers whose product is 4 and sum is -5

• Find two numbers whose product is -5 and sum is 4

Which pair of numbers correctly factors the expression x^2 + 4x - 5?

• 1 and -5

• -1 and 5

• 2 and -3

• -2 and 3

What is the factored form of x^2 + 4x - 5?

• (x + 1)(x - 5)

• (x - 1)(x + 5)

• (x + 2)(x - 3)

• (x - 2)(x + 3)

When factoring expressions with two variables, what is important to remember?

• The process is completely different

• The process is fundamentally the same

• You must always factor out a common term first

• You should ignore the second variable

What is the first step in factoring x^2 + 4xy - 5y^2?

• Find two numbers whose product is 5y^2

• Find two numbers whose product is 4y

• Find two terms whose product is -5y^2 and sum is 4y

• Find two terms whose sum is -5y^2

Which pair of terms correctly factors the expression x^2 + 4xy - 5y^2?

• -2y and 3y

• 2y and -3y

• -y and 5y

• y and -5y

What is the factored form of x^2 + 4xy - 5y^2?

• (x + 2y)(x - 3y)

• (x - y)(x + 5y)

• (x - 2y)(x + 3y)

• (x + y)(x - 5y)

What is the result of multiplying (x - y)(x + 5y)?

• x^2 + 5xy - y^2

• x^2 + 4xy - 5y^2

• x^2 - 4xy + 5y^2

• x^2 + 4xy + 5y^2

What is the coefficient of the x term in the expression x^2 + 4xy - 5y^2?

• 5y

• 4y

• 5

• 4

What does the term -5y^2 correspond to in the expression x^2 + 4xy - 5y^2?

• The product term

• The constant term

• The coefficient of x

• The coefficient of y