Factoring Quadratics: When It Can't Be Done

What is the primary goal when factoring a quadratic equation like x^2 - 16x + 51?

• Find two numbers that multiply to 51 and add to -16

• Find two numbers that multiply to -51 and add to 16

• Find two numbers that multiply to -16 and add to 51

• Find two numbers that multiply to 16 and add to 51

What are the two numbers you need to find when factoring a quadratic like x^2 - 16x + 51?

• Numbers that multiply to -51 and add to 16

• Numbers that multiply to 16 and add to -51

• Numbers that multiply to -16 and add to 51

• Numbers that multiply to 51 and add to -16

What does it indicate if no pair of numbers can be found that meet the factoring requirements of a quadratic equation?

• The quadratic is likely unfactorable

• The quadratic is incomplete

• The quadratic needs a different method

• The quadratic is definitely factorable

What does it mean if a quadratic cannot be factored using any method?

• It is unfactorable

• It is an error in the equation

• It requires a higher level of math

• It is incomplete

What should you assume about a quadratic problem before starting to factor it?

• It is unfactorable

• It is always factorable

• It might be factorable

• It requires numerical methods

Why might humans fail to factor a quadratic correctly?

• Because the numbers are too large

• Because the method used is incorrect

• Because the quadratic is always solvable

• Due to human error and oversight

What is the correct approach when starting to factor a quadratic equation?

• Use graphical methods first

• Start with complex numbers

• Assume it is unfactorable

• Assume it is factorable unless proven otherwise

What is the 'Magic X' method used for in quadratic factoring?

• To factor quadratics with any coefficients

• To factor quadratics with a leading coefficient greater than one

• To factor linear equations

• To solve quadratic equations

What does the top number in the 'Magic X' represent?

• Difference between the leading coefficient and the constant

• Quotient of the leading coefficient and the constant

• Sum of the leading coefficient and the constant

• Product of the leading coefficient and the constant

What should you do if you cannot find factors that meet the requirements of the 'Magic X' method?

• All of the above

• Check for calculation errors

• Try a different mathematical approach

• Assume the quadratic is unfactorable