Unit 2, Lesson 4
Combining Polynomials
Integrated Math 3
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What do you notice? What do you wonder?
Which of these statements are true? Give reasons in support of your answer.
Here are some questions about polynomials. You and a partner will work on one of these questions.
If we add two integers, subtract one from the other, or multiply them, the result is another integer. The same is true for polynomials: Combining polynomials by addition, subtraction, or multiplication will always give us another polynomial.
For example, we can multiply and . We can use the distributive property and keep track of the results using a diagram like this:
| 4.5 |
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Then we can find the product by adding all the results we filled in. This diagram tells us that the product is , which is also a polynomial even though there are square roots as coefficients! No matter what polynomials we start with, multiplying them will give us a polynomial. Adding or subtracting polynomials also gives us a polynomial, because we are just combining like terms.
When thinking about polynomials, it is important to remember exactly what counts as a polynomial. Any sum of terms that all have the same variable, where the variable is only raised to non-negative integer powers, is a polynomial. So some things that might not look like polynomials at first, such as -34.1 or , are polynomials.