Montana Math MT.PLUS.ALG.POLY.2.c
The Standard
- MT.PLUS.ALG.POLY.2
- Understand that polynomial expressions can be represented in both factored and standard form, and the specific features of each form by: Choosing the form strategically based on given information and intended use when writing an expression, Converting between factored and standard form symbolically and using representations (e.g., area model), and Interpreting the relationship between the factored form of the expression and the zeros of the function.
Understand that polynomial expressions can be represented in both factored and standard form, and the specific features of each form by: Interpreting the relationship between the factored form of the expression and the zeros of the function.
2026 Montana Mathematics Content Standards · Algebraic and Functional Reasoning
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students find the values of x that make a polynomial equal zero by looking at its factors. They connect those values to where the graph meets the x-axis, even when the polynomial is also written in standard form.
What Mastery Looks Like
- Given (x-2)(x+3), a student identifies 2 and -3 as zeros and checks them by substitution. They can expand the expression to x²+x-6 and explain why the zeros stay the same.
Common Misconceptions
- Students may read (x-2) as a zero of -2 instead of 2. They may confuse zeros with y-intercepts or think expanding the expression changes its zeros.
How to Assess It
- Exit ticket: For f(x)=(x-3)(x+2), list both zeros, check one by substitution, and explain whether expanding changes the zeros.
Lesson moves
Ways to Teach It
Give students cards labeled (x-2), (x+3), x²+x-6, 2, and -3; have them group the matching forms and zeros.
Ask students to write why (x-4)(x+1)=0 gives 4 and -1, using substitution to support their answer.
Play zero bingo with cards numbered -5 to 5: show factored quadratics and have students cover each zero.
Give students h(t)=-5t(t-4) for a thrown ball; have them mark its launch and landing times on a timeline.
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Related Standards
- MT.CORE.ALG.QUAD.3
Understand that quadratic expressions can be represented in multiple forms and the specific features of each form by: Choosing the form strategically when writi...
- MT.PLUS.ALG.POLY.2
Understand that polynomial expressions can be represented in both factored and standard form, and the specific features of each form by: Choosing the form strat...
- MT.CORE.ALG.QUAD.3.d
Understanding the relationship between vertex form and the vertex of the function.
- MT.CORE.ALG.QUAD.3.c
Understanding the relationship between factored form and the zeros of the function, and
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