Completing the Square Techniques

Professor Dave explains the technique of completing the square, a method for solving polynomials that cannot be factored. He demonstrates this with examples, showing how to transform a polynomial into a perfect square trinomial, making it easier to solve. The process involves manipulating the equation to create a perfect square on one side, allowing for straightforward solutions. The video covers different scenarios, including polynomials with coefficients on the X² term, and emphasizes the importance of this technique in solving complex polynomials.

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

• It always results in integer solutions.

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

• It is faster than factoring.

• It only works for quadratic polynomials.

What is the result of factoring the polynomial X squared plus two X plus one?

• X minus one times X minus one

• X plus one times X plus one

• X plus two times X plus two

• X plus two times X minus one

When completing the square for X squared plus two X minus six, what term is added to both sides to form a perfect square?

• Zero

• Six

• Two

• One

In the example X squared plus six X minus two, what is the value of the term added to complete the square?

• Six

• Nine

• Three

• Twelve

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

• Multiply the entire equation by the coefficient

• Add the coefficient to both sides

• Divide the entire equation by the coefficient

• Subtract the coefficient from both sides

In the example with three X squared plus fifteen X minus eight, what is the first step after moving the constant to the other side?

• Multiply everything by three

• Divide everything by three

• Add eight to both sides

• Subtract eight from both sides

What is the least common denominator used in the example with fractions?

• Four

• Sixteen

• Eight

• Twelve

What is the final step in solving a completed square equation?

• Take the square root of both sides and solve for X

• Subtract the square root from both sides

• Multiply both sides by the square root

• Add the square root to both sides

What should you do if the solutions to a completed square equation are not neat and tidy?

• Round them to the nearest integer

• Accept them as they are

• Ignore them

• Multiply them by a common factor

What is the purpose of cutting the X coefficient in half when completing the square?

• To eliminate the X term

• To simplify the equation

• To determine the factor in the binomial

• To find the constant term