Factoring and Quadratic Equations flashcards

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What does monic trinomials mean?Factoring Trinomials: A pair of binomial factors for a leading coefficient of one.
Why check both sum and product?Factoring Trinomials: Each controls a different coefficient.
How would you define negative constants?Factoring Trinomials: A sign clue for integer trinomial factors.
Does a negative c guarantee integer factors?Factoring Trinomials: No, integer factors may not satisfy the required sum.
What is meant by checking factors?Factoring Trinomials: Verifying a proposed polynomial factorization.
Should unsupported factors be invented?Factoring Trinomials: No, choose another solving method if needed.
What does recognizing squares mean?Difference of Squares: A pattern factored with conjugates.
Does A²+B² use the same real factorization?Difference of Squares: No, the real difference-of-squares rule needs subtraction.
How would you define conjugate factors?Difference of Squares: Two binomials differing only in the middle sign.
Why does the middle term vanish?Difference of Squares: AB and −AB cancel.
What is meant by repeated factoring?Difference of Squares: Checking whether a factorization is complete over the intended number system.
Why specify the number system?Difference of Squares: Further factors available over complex numbers may differ from real factors.
What does zero product mean?Zero-Product Property: The equation-solving rule for zero products.
Can it be applied directly when a product equals five?Zero-Product Property: No, first rewrite the equation with zero on one side.
How would you define solving factored quadratics?Zero-Product Property: Finding all roots of a factored quadratic.
Why solve both factor equations?Zero-Product Property: Either factor may be zero.
What is meant by finding x-intercepts?Zero-Product Property: Connecting algebraic roots to coordinate intercepts.
Can a quadratic have no real x-intercepts?Zero-Product Property: Yes, if it never reaches y=0.
What does creating a perfect square mean?Completing the Square: A step turning a quadratic expression into a squared binomial.
Why add the same amount to both sides?Completing the Square: To preserve the equation while completing the square.
How would you define solving with square roots?Completing the Square: Recovering both solutions from a squared equation.
How many real roots can k<0 yield?Completing the Square: None for a real square.
What is meant by vertex form?Completing the Square: A quadratic form exposing the turning point.
What does a negative a do?Completing the Square: It opens the parabola downward.
What does quadratic formula mean?Quadratic Formula and Discriminant: A general solution rule for quadratic equations.
Why require a≠0?Quadratic Formula and Discriminant: Otherwise the equation is not quadratic and the denominator is zero.
How would you define discriminant?Quadratic Formula and Discriminant: A root-count test inside the quadratic formula.
Does a negative discriminant give real roots?Quadratic Formula and Discriminant: No, its square root is not real.
What is meant by checking and choosing methods?Quadratic Formula and Discriminant: Comparing equivalent routes to the same roots.
Why might the formula be useful?Quadratic Formula and Discriminant: It works even when integer factoring is unavailable.