Completing the Square with a Leading Coefficient Not Equal to 1: Algebraic

This video tutorial teaches how to complete the square in quadratic expressions with non-unit leading coefficients. It begins with an introduction to the concept, followed by a detailed explanation of the distributive property. Two examples are provided to demonstrate the process of completing the square, including factoring and adjusting the expression to maintain equality. The lesson concludes with a summary of the key points covered.

What is a common mistake when using the distributive property to multiply a monomial by a polynomial?

• Not using the monomial at all

• Multiplying the monomial by the polynomial twice

• Multiplying the monomial by only some terms of the polynomial

• Forgetting to multiply the monomial by the first term

In the expression 2x^2 + 20x + 1, what number completes the square after factoring out the 2?

• 5

• 50

• 25

• 10

After completing the square for 2x^2 + 20x + 1, what is the vertex form of the expression?

• 2(x - 5)^2 - 49

• 2(x - 5)^2 + 49

• 2(x + 5)^2 - 49

• 2(x + 5)^2 + 49

In the expression 3x^2 - 4x - 2, what is the linear coefficient after factoring out the 3?

• -3/4

• -1/3

• -2

• -4/3

What is the vertex form of the expression 3x^2 - 4x - 2 after completing the square?

• 3(x - 2/3)^2 - 10/3

• 3(x + 2/3)^2 + 10/3

• 3(x + 2/3)^2 - 10/3

• 3(x - 2/3)^2 + 10/3