NY Next Generation Math AII-A.APR.3
The Standard
Identify zeros of polynomial functions when suitable factorizations are available.
New York State Next Generation Mathematics Learning Standards
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students identify zeros of Algebra II polynomial functions when the polynomial has a usable factorization. They connect each factor, zero, and x-intercept.
What Mastery Looks Like
- The student factors or uses a supplied factorization, applies the zero-product property, and lists all real zeros represented. Substitution or a graph confirms the results.
Common Misconceptions
- Students may set the whole polynomial equal to each coefficient, lose repeated zeros, or report factors instead of zero values. They may attempt unsupported factoring when no suitable form is available.
How to Assess It
- Give f(x) equals (x minus 2) squared times (x plus 3). Ask students for all zeros, multiplicities, and corresponding x-intercepts.
Lesson moves
Ways to Teach It
Match factor cards, zero cards, and x-intercept cards for several polynomial functions.
Ask students how a repeated factor affects the zero list and the graph near that intercept.
Play zero-product relay by factoring suitable polynomials and passing each factor to a solver.
Find break-even input values from a factored polynomial profit model.
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Related Standards
- AI-A.APR.1
Add, subtract, and multiply polynomials and recognize that the result of the operation is also a polynomial. This forms a system analogous to the integers.
- AI-A.SSE.1.a
Write the standard form of a given polynomial and identify the terms, coefficients, degree, leading coefficient, and constant term.
- AI-F.IF.8.a
For a quadratic function, use an algebraic process to find zeros, maxima, minima, and symmetry of the graph, and interpret these in terms of context.
- AII-F.IF.7.c
Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.
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