Algebra 1
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.