Curriculum placement
Algebra 2. This describes the skill, not a learner estimate.
Zeros and factors of a polynomial
Connect factors zeros and polynomial graphs
Problem types
- Zeros of a nonmonic product or a cubic by grouping
- Solve a polynomial inequality
- Enter a zero of a factored polynomial
- Zeros from factors
- Crossing or touching at a zero
- Find all zeros of a product containing a difference of squares
- Choose the polynomial rule that matches a graph with a repeated zero
Builds on
- Calculating with complex numbers
- Dividing polynomials
- Fundamental theorem of algebra · Earlier idea
A polynomial of degree n has n complex zeros counted with multiplicity, which is used to count and find zeros.
- The conjugate of a complex number · Useful idea
Nonreal zeros of a polynomial with real coefficients come in conjugate pairs.
- Factoring over the complex numbers · Useful idea
Writing a polynomial as a product of complex linear factors shows each zero and its multiplicity.
- Regions defined by inequalities · Earlier idea
A polynomial inequality is solved by the signs between zeros, as a half-plane is found by testing a point on each side of a line.
- The quadratic formula · Earlier idea
The quadratic formula gives zeros of a degree-two polynomial, and the discriminant tells whether a zero repeats.
Leads to
- Linear growth against exponential growth
- End behavior of a polynomial
- Values a rational expression excludes · See it applied
The zeros of the denominator polynomial are the values excluded from the domain of a rational expression.
Related skills
- How many times a line meets a curve · Related idea
The intersections of two graphs are the zeros of the difference of their equations, and the number of zeros is bounded by the degree.
- The complex plane · Shared foundations
Open the interactive map to explore lessons and skill connections.