Montana Math MT.PLUS.ALG.POLY.1

MathGrades 9–12Polynomial Functions

The Standard

Understand polynomials are created by multiplying linear factors.

2026 Montana Mathematics Content Standards · Algebraic and Functional Reasoning

Teacher's field guide

What Students Need to Do: Students multiply linear expressions to make a polynomial. They connect each factor to a value of x that makes the product zero, and recognize the product in expanded form.
What Mastery Looks Like: Given (x − 2)(x + 3), a student expands it to x² + x − 6 and identifies 2 and −3 as zeros. They can factor x² + x − 6 back and check by multiplying.
Common Misconceptions: Students may add the factors instead of multiplying them, or leave out the middle term when expanding. They may say the zero of x − 2 is −2 because they read the sign without solving x − 2 = 0.
How to Assess It: On an exit ticket, ask: Expand (x − 2)(x + 3). What are its zeros, and how can you tell from the factors?

Lesson moves

Use algebra tiles to build a rectangle with sides x + 2 and x + 3, then record its area as a polynomial.
Ask students to write why x − 2 gives a zero of 2, not −2.
Give pairs cards showing products and expanded polynomials; have them match cards and check each match by multiplying.
Draw a garden with side lengths x + 2 and x + 3 feet; have students write two forms of its area.

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