This really is a polynomial even it may not look like

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Unformatted text preview: polynomial. Note that we will often drop the “in one variable” part and just say polynomial. Here are examples of polynomials and their degrees. 5 x12 - 2 x 6 + x5 - 198 x + 1 degree : 12 x4 - x3 + x2 - x + 1 degree : 4 23 56 x 5x - 7 -8 degree : 23 degree : 1 degree : 0 So, a polynomial doesn’t have to contain all powers of x as we see in the first example. Also, polynomials can consist of a single term as we see in the third and fifth example. We should probably discuss the final example a little more. This really is a polynomial even it may not look like one. Remember that a polynomial is any algebraic expression that consists of terms in the form ax n . Another way to write the last example is -8 x 0 Written in this way makes it clear that the exponent on the x is a zero (this also explains the degree…) and so we can see that it really is a polynomial in one variable. Here are some examples of things that aren’t polynomials. 4 x 6 + 15 x -8 + 1 5 x - x + x2 23 + x -2 x The first one isn’t a polynom...
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