Unit 12 · Polynomials, Modeling & Comparison

Polynomial Operations

Combine like terms to add/subtract. Multiply with the distributive property (or a table). Degree adds when multiplying monomials.

Algebra I Regents

AI-A.APR.1AI-A.SSE.1

Notes

3x² and 5x² combine; 3x² and 5x do not. Subtracting a polynomial means distributing the minus to every term.

A sum of terms of the form ax^n where n is a whole number.

Example: 4x³ − x + 7 is a cubic polynomial.

Try the prompt first. The steps stay folded until you ask to see them.

(x + 3)(x − 5)

Watch for

Writing (x + 3)² = x² + 9

The middle term 2·x·3 is missing.

Fix: Always write (x + 3)(x + 3).

Submit each answer to check it. The key is not shown until you do.

Question 1 of 3Algebra I RegentsAI-A.APR.1Algebra I Regents · June 2024 · Q8Non-calculatoremerging

What is the degree of the polynomial 2x − x² + 4x³?

1234

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Question 2 of 3Algebra I RegentsAI-A.APR.1Algebra I Regents · June 2024 · Q4Non-calculatorproficient

The expression −2(x² − 2x + 1) + (3x² + 3x − 5) is equivalent to

x² + x − 4x² − x − 7x² + 7x − 4x² + 7x − 7

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Question 3 of 3Algebra I RegentsAI-A.APR.1Algebra I Regents · June 2024 · Q19Non-calculatorproficient

Which expression is equivalent to (x − 5)(2x + 7) − (x + 5)?

2x² − 2x − 302x² − 2x − 402x² − 4x − 302x² − 4x − 40

Choose or type an answer first. The key stays hidden until you do.

Use an area model (box method) for every product.

Explain why the product of two linear factors is quadratic.

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