Full unit practice requiring complete reasoning and representation checks.
Directions: Show exact work before decimals, label domains or intervals, and explain calculator use.
1. {'id': 'u02-l01', 'number': 1, 'title': 'Power Functions and Polynomial End Behavior', 'family': 'polynomial', 'week': 4, 'unit': 2, 'unit_title': 'Polynomial & Rational Functions', 'essential': 'How do algebraic structure, zeros, multiplicity, asymptotes, and rates of change determine polynomial and rational behavior?', 'project': 'Polynomial-Rational Design Specification'}
State the end behavior of f(x)=−3x⁴+2x.
2. {'id': 'u02-l01', 'number': 1, 'title': 'Power Functions and Polynomial End Behavior', 'family': 'polynomial', 'week': 4, 'unit': 2, 'unit_title': 'Polynomial & Rational Functions', 'essential': 'How do algebraic structure, zeros, multiplicity, asymptotes, and rates of change determine polynomial and rational behavior?', 'project': 'Polynomial-Rational Design Specification'}
Find the zeros of (x−2)²(x+5).
3. {'id': 'u02-l01', 'number': 1, 'title': 'Power Functions and Polynomial End Behavior', 'family': 'polynomial', 'week': 4, 'unit': 2, 'unit_title': 'Polynomial & Rational Functions', 'essential': 'How do algebraic structure, zeros, multiplicity, asymptotes, and rates of change determine polynomial and rational behavior?', 'project': 'Polynomial-Rational Design Specification'}
How does the graph behave at x=2 for (x−2)²(x+5)?
4. {'id': 'u02-l01', 'number': 1, 'title': 'Power Functions and Polynomial End Behavior', 'family': 'polynomial', 'week': 4, 'unit': 2, 'unit_title': 'Polynomial & Rational Functions', 'essential': 'How do algebraic structure, zeros, multiplicity, asymptotes, and rates of change determine polynomial and rational behavior?', 'project': 'Polynomial-Rational Design Specification'}
Divide x³−4x²+x+6 by x−2.
5. {'id': 'u02-l01', 'number': 1, 'title': 'Power Functions and Polynomial End Behavior', 'family': 'polynomial', 'week': 4, 'unit': 2, 'unit_title': 'Polynomial & Rational Functions', 'essential': 'How do algebraic structure, zeros, multiplicity, asymptotes, and rates of change determine polynomial and rational behavior?', 'project': 'Polynomial-Rational Design Specification'}
Find the remainder when f(x)=x³+2x−1 is divided by x−3.
6. {'id': 'u02-l01', 'number': 1, 'title': 'Power Functions and Polynomial End Behavior', 'family': 'polynomial', 'week': 4, 'unit': 2, 'unit_title': 'Polynomial & Rational Functions', 'essential': 'How do algebraic structure, zeros, multiplicity, asymptotes, and rates of change determine polynomial and rational behavior?', 'project': 'Polynomial-Rational Design Specification'}
What is the maximum possible number of turning points of a degree-6 polynomial?
7. {'id': 'u02-l02', 'number': 2, 'title': 'Zeros, Factors & Multiplicity', 'family': 'polynomial', 'week': 4, 'unit': 2, 'unit_title': 'Polynomial & Rational Functions', 'essential': 'How do algebraic structure, zeros, multiplicity, asymptotes, and rates of change determine polynomial and rational behavior?', 'project': 'Polynomial-Rational Design Specification'}
State the end behavior of f(x)=−3x⁴+2x.
8. {'id': 'u02-l02', 'number': 2, 'title': 'Zeros, Factors & Multiplicity', 'family': 'polynomial', 'week': 4, 'unit': 2, 'unit_title': 'Polynomial & Rational Functions', 'essential': 'How do algebraic structure, zeros, multiplicity, asymptotes, and rates of change determine polynomial and rational behavior?', 'project': 'Polynomial-Rational Design Specification'}
Find the zeros of (x−2)²(x+5).
9. {'id': 'u02-l02', 'number': 2, 'title': 'Zeros, Factors & Multiplicity', 'family': 'polynomial', 'week': 4, 'unit': 2, 'unit_title': 'Polynomial & Rational Functions', 'essential': 'How do algebraic structure, zeros, multiplicity, asymptotes, and rates of change determine polynomial and rational behavior?', 'project': 'Polynomial-Rational Design Specification'}
How does the graph behave at x=2 for (x−2)²(x+5)?
10. {'id': 'u02-l02', 'number': 2, 'title': 'Zeros, Factors & Multiplicity', 'family': 'polynomial', 'week': 4, 'unit': 2, 'unit_title': 'Polynomial & Rational Functions', 'essential': 'How do algebraic structure, zeros, multiplicity, asymptotes, and rates of change determine polynomial and rational behavior?', 'project': 'Polynomial-Rational Design Specification'}
Divide x³−4x²+x+6 by x−2.
11. {'id': 'u02-l02', 'number': 2, 'title': 'Zeros, Factors & Multiplicity', 'family': 'polynomial', 'week': 4, 'unit': 2, 'unit_title': 'Polynomial & Rational Functions', 'essential': 'How do algebraic structure, zeros, multiplicity, asymptotes, and rates of change determine polynomial and rational behavior?', 'project': 'Polynomial-Rational Design Specification'}
Find the remainder when f(x)=x³+2x−1 is divided by x−3.
12. {'id': 'u02-l02', 'number': 2, 'title': 'Zeros, Factors & Multiplicity', 'family': 'polynomial', 'week': 4, 'unit': 2, 'unit_title': 'Polynomial & Rational Functions', 'essential': 'How do algebraic structure, zeros, multiplicity, asymptotes, and rates of change determine polynomial and rational behavior?', 'project': 'Polynomial-Rational Design Specification'}
What is the maximum possible number of turning points of a degree-6 polynomial?