Solving Quadratics by Completing the Square

The video tutorial explains the technique of completing the square, a method used to solve polynomials that cannot be factored. It begins with an introduction to the concept, followed by examples demonstrating how to factor perfect square polynomials and how to complete the square for non-factorable polynomials. The tutorial also covers handling polynomials with a coefficient on the x-squared term, emphasizing the importance of maintaining balance by performing operations on both sides of the equation.

What is the result when you factor the polynomial x-squared plus 2x plus 1?

• x minus 1 times x minus 1

• x plus 2 times x minus 1

• x plus 1 times x plus 1

• x plus 3 times x minus 2

Why is completing the square a useful technique for solving polynomials?

• It simplifies the polynomial to a linear equation.

• It can solve any polynomial, even if it cannot be factored.

• It always results in integer solutions.

• It only works for polynomials with even coefficients.

In the example x-squared plus 2x minus 6 equals 0, what is added to both sides to complete the square?

• 1

• 2

• 6

• 3

When completing the square for x-squared plus 6x minus 2 equals 0, what value is added to both sides?

• 6

• 9

• 3

• 12

What is the first step when completing the square for a polynomial with a coefficient on the x-squared term?

• Subtract the coefficient from both sides.

• Divide everything by the coefficient.

• Add the coefficient to both sides.

• Multiply everything by the coefficient.

In the example 3x squared plus 15x minus 8 equals 0, what is the least common denominator used to combine fractions?

• 24

• 8

• 16

• 12

What is the final form of the left side of the equation after completing the square for 3x squared plus 15x minus 8 equals 0?

• x plus 3/2 quantity squared

• x plus 5/2 quantity squared

• x plus 4/2 quantity squared

• x plus 6/2 quantity squared