CCSS.Math.Content.HSA-APR.B

CCSS.Math.Content.HSA-APR.B is a cluster heading. These are the individual standards under it.

• CCSS.Math.Content.HSA-APR.B.2

  Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x - a is p(a), so p(a) = 0 if and only if (x - a) is a ...

• 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...

01

What Students Need to Do

Students connect a polynomial’s zeros with its linear factors. They use substitution, factoring, or polynomial division to find zeros and explain what those zeros show on a graph.

02

What Mastery Looks Like

Students use substitution or division to confirm whether a given expression is a factor. They factor polynomials, identify all zeros, and connect real zeros to x-intercepts on a graph.

03

Common Misconceptions

Students may confuse a zero, such as 3, with its factor, which is x minus 3. They may rely only on a graph and miss repeated or nonreal zeros. Some assume every polynomial factors into integers.

04

How to Assess It

Give p(x) = x³ - 4x² - x + 4. Ask students to test x - 4, factor p(x) completely, list its zeros, and sketch its x-intercepts.

1. 01

   Give groups cards showing polynomials, factored forms, zeros, and graphs, then have them build matching sets and explain each match.

2. 02

   Ask students to explain why p(5) = 0 guarantees that x - 5 divides p(x) evenly.

3. 03

   Run a factor relay where teams test possible zeros, divide the polynomial, and pass the quotient to the next teammate.

4. 04

   Use h(t) = -16t² + 48t for a launched ball, then factor it and interpret both zeros as times.

• 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.