Factoring Quadratics by Inspection

What is a primary method used to solve quadratic equations?

• Applying the distributive property

• Factoring into linear expressions

• Graphing the equation

• Using the Pythagorean theorem

What are special products in the context of quadratic expressions?

• Quadratic formulas

• Difference of squares and perfect squares

• Linear expressions

• Graphical intersections

What makes factoring straightforward when a quadratic expression has no constant term?

• The discriminant is always positive

• There are no real solutions

• The quadratic formula simplifies

• One linear factor is always x

What does the zero product property imply about the solutions of a quadratic equation?

• They are always positive

• They are the zeros of the quadratic function

• They can only be found graphically

• They do not exist

What is required for factoring by inspection when all constants a, b, and c are non-zero?

• Trial and error

• Completing the square

• Using the quadratic formula

• Graphing the quadratic function

What simplifies the task of factoring by inspection?

• Having the coefficient of x-squared equal to one

• Knowing the quadratic formula

• Using a graphing calculator

• Having no constant term

How do you determine the factors of a quadratic expression when the coefficient of x-squared is one?

• By using the quadratic formula

• By finding integer values for q and s

• By applying the difference of squares

• Through graphing the quadratic

What is the result of substituting the solution back into the quadratic equation?

• A true statement verifying the solution

• A linear equation

• A new quadratic equation

• An undefined expression

Why might factoring by inspection not be possible for some quadratics?

• The solutions are not integers

• The quadratic has no real solutions

• All solutions are negative

• The coefficient of x-squared is not one

What alternative methods are suggested for factoring quadratics when inspection fails?

• Simplifying the expression

• Graphing the function

• Completing the square or using the quadratic formula

• Applying the Pythagorean theorem