Montana Math MT.PLUS.ALG.POLY.2.a
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: Choosing the form strategically based on given information and intended use when writing an expression,
2026 Montana Mathematics Content Standards · Algebraic and Functional Reasoning
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students write a polynomial in factored or standard form based on the information they have. They choose the form that makes the feature they need easiest to find.
What Mastery Looks Like
- Given zeros of 2 and −3 and a y-intercept of −12, a student writes 2(x−2)(x+3), then expands it to 2x²+2x−12. They explain why factored form shows the zeros and standard form shows the y-intercept.
Common Misconceptions
- Students may call −3 a zero of (x−3) or mistake a number inside a factor for the y-intercept. They may assume the zeros alone determine the leading coefficient, or think expanding changes the polynomial.
How to Assess It
- Exit ticket: A quadratic has zeros of 1 and −4 and a y-intercept of −8. Write it in factored and standard form, then explain which form shows each feature most clearly.
Lesson moves
Ways to Teach It
Hand out cards labeled 2, (x−2), and (x+3); students build the product and expand it on mini whiteboards.
Put 2(x−2)(x+3) beside 2x²+2x−12; ask which form helps find the zeros and which shows the y-intercept.
Give groups equivalent-expression cards and question cards about zeros or y-intercepts; race to select the most useful form.
A club's profit is P(x)=−2(x−10)(x−50), where x is tickets sold; find break-even sales, then expand to find the startup cost.
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