Factoring Quadratics: Key Concepts and Techniques

What is the first step in solving a quadratic equation by completing the square?

• Take the square root of both sides

• Divide all terms by the coefficient of x^2

• Factor out the greatest common factor

• Move the constant term to the right side

What must be true about the coefficient of x^2 when completing the square?

• It must be zero

• It must be one

• It must be negative

• It can be any number

How do you adjust the equation if the coefficient of x^2 is not 1 when completing the square?

• Subtract the coefficient from both sides

• Divide all terms by the coefficient

• Multiply all terms by the coefficient

• Add the coefficient to both sides

What do you do after adding the square of half the coefficient of x to both sides in completing the square?

• Divide by the leading coefficient

• Factor the perfect square trinomial

• Simplify the right side of the equation

• Take the square root of both sides

What is the result of completing the square for the equation x^2 + 6x + 9 = 0?

• (x + 3)^2

• (x - 3)^2

• x^2 + 3

• x^2 - 3

When solving x^2 + 2x + 1 = 0 by completing the square, what is the value of x?

• -1

• 2

• 1

• 0

When using the quadratic formula, what is the value of 'b' in the equation ax^2 + bx + c = 0?

• The coefficient of x^2

• The constant term

• The discriminant

• The coefficient of x

What is the discriminant in the quadratic formula?

• b^2 - 4ac

• b^2 + 4ac

• 2a

• -b/2a

Which method would you likely choose if the coefficient of x does not divide evenly by 2?

• Graphing

• Completing the square

• Quadratic formula

• Factoring

In the quadratic formula, what does '2a' in the denominator represent?

• The vertex of the parabola

• The sum of the roots

• The double of the leading coefficient

• The axis of symmetry