Completing the Square Made Easy

The video tutorial explains the technique of completing the square, a method used when polynomials do not factor easily. It outlines the steps: taking half of the x term's coefficient, squaring it, and adding zero by adding and subtracting the same number. The goal is to transform the polynomial into a perfect square plus a constant. Two examples are provided to illustrate the process, demonstrating how to factor the polynomial and combine constants to achieve the perfect square form.

What is the main goal of completing the square?

• To simplify the polynomial

• To factor the polynomial completely

• To break down the polynomial into a perfect square plus a constant

• To find the roots of the polynomial

What is the first step in completing the square?

• Take half of the x coefficient

• Add zero

• Combine constants

• Square the x coefficient

If the x coefficient is 2, what is half of it?

• 0.5

• 4

• 2

• 1

What do you do after taking half of the x coefficient?

• Add zero

• Square it

• Combine constants

• Factor the polynomial

What does 'adding zero' mean in the context of completing the square?

• Ignoring the constant term

• Multiplying by zero

• Adding zero to the polynomial

• Adding and subtracting the same number

What is the result of combining x squared plus 2x plus 1 minus 1 plus 3?

• x + 1 squared plus 2

• x + 2 squared plus 1

• x squared plus 2x plus 4

• x squared plus 2x plus 1

In the second example, what is half of the x coefficient 6?

• 9

• 6

• 2

• 3

What is 3 squared?

• 3

• 9

• 12

• 6

What is the final form of the polynomial x squared plus 6x plus 9 minus 9 plus 11?

• x + 3 squared plus 2

• x + 6 squared plus 2

• x squared plus 6x plus 2

• x squared plus 6x plus 11

What is the purpose of completing the square?

• To break down the polynomial into a perfect square plus a constant

• To find the roots of the polynomial

• To simplify the polynomial

• To factor the polynomial completely