CCSS.Math.Content.HSA-APR.B
The standard
Understand the relationship between zeros and factors of polynomials
Common Core State Standards for Mathematics · High School — Algebra
What this standard means
Students need to connect a polynomial’s zeros, x-intercepts, and factors. If x = 3 is a zero, they should know x - 3 is a factor. They should also use factoring, graphs, tables, and division to move between forms and explain why the connection works.
Mastery looks like identifying zeros from a factored polynomial, writing factors from given zeros, and checking by substitution or graphing. Students often mix up signs, confuse zeros with y-intercepts, or think every polynomial factors nicely over the integers.
Ways to teach it
- Use algebra tiles or area models to factor a quadratic, then match each factor to the graph’s x-intercepts.
- Ask students to explain why x = -4 means x + 4 is a factor, using numbers, not memorized rules.
- Give three polynomials in factored form and ask students to list zeros, then verify one by substitution.
- Show a projectile height equation and ask when the object hits the ground, connecting the time value to a zero.
Plan a lesson for CCSS.Math.Content.HSA-APR.B
Generate a complete lesson plan aligned to this standard, with objectives, activities, and materials. Free, no account needed.
Related standards
- CCSS.Math.Content.HSA-APR.B.3
Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial...
- CCSS.Math.Content.HSF-IF.C.8a
Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in ...
- CCSS.Math.Content.HSF-IF.C.7c
Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.
- CCSS.Math.Content.HSA-SSE.B.3a
Factor a quadratic expression to reveal the zeros of the function it defines.