Unit 3 Honors Math 3: Review of Polynomials

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Mathematics
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10th - 12th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
What are the zeros of a polynomial?
Back
The zeros of a polynomial are the values of x for which the polynomial equals zero. They can be found by solving the equation p(x) = 0.
2.
FLASHCARD QUESTION
Front
What is multiplicity in relation to polynomial zeros?
Back
Multiplicity refers to the number of times a particular zero appears as a root of the polynomial. A zero with an even multiplicity will touch the x-axis, while a zero with an odd multiplicity will cross the x-axis.
3.
FLASHCARD QUESTION
Front
How do you find the zeros of the polynomial g(x) = (x+4)^2(x+8)^3(x-5)?
Back
Set g(x) = 0 and solve for x: The zeros are x = -4 (multiplicity 2), x = -8 (multiplicity 3), and x = 5 (multiplicity 1).
4.
FLASHCARD QUESTION
Front
What is the quadratic formula?
Back
The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the solutions of the quadratic equation ax² + bx + c = 0.
5.
FLASHCARD QUESTION
Front
What are complex roots?
Back
Complex roots are solutions to polynomial equations that include imaginary numbers. They occur in conjugate pairs when coefficients are real.
6.
FLASHCARD QUESTION
Front
How do you determine the intervals where a polynomial is increasing or decreasing?
Back
To find increasing or decreasing intervals, analyze the first derivative of the polynomial. Increasing intervals occur where the derivative is positive, and decreasing intervals occur where the derivative is negative.
7.
FLASHCARD QUESTION
Front
What does it mean for a polynomial to have a zero with a wave behavior?
Back
A zero with wave behavior occurs when the multiplicity of the zero is odd, causing the graph to cross the x-axis at that point.
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