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a. Write $x-9+3 x^{2}+5 x^{3}$ in descending powers of $x$b. Write $-2 x y+y^{2}+x^{2}$ in ascending powers of $y$
a. $5 x^{3}+3 x^{2}+x-9$b. $x^{2}-2 x y+y^{2}$
Algebra
Chapter 5
Exponents and Polynomials
Section 4
Polynomials
Campbell University
Oregon State University
Harvey Mudd College
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all right. So for the first polynomial, we're going to rewrite it so that we have descending powers of X. So let's look at all the terms when we see exit means X to the first. When we see a constant like negative nine, it means negative nine x to the zero. And then we see in the third term three x squared the powers to and in the fourth term five x cube the powers three. So descending means from highest to lowest on the highest is three. So we're starting with five x cubed and then the next one down plus three x squared and then the next one down plus X and then the last one minus nine Those air now in descending powers of X, the second expression has both exes and wise, and we're going to put the terms in ascending powers of why ah, sending means going up. So we want the smallest power of life first and the highest power of why last looking at these terms, the first term has why in it that would be why, to the first, the second term has y squared. So why score is gonna be the highest power we see here in this one and then the third term just has an X squared. So you can think of that as a white to the zero. Because why, to the zero is just one so, uh, sending powers of why Starting with the smallest would be the X squared term. The one that has the invisible. Why, to the zero on it. And then the next one up would be the negative to X Y. Since that has White of the first and then the 3rd 1 would be y squared, since that's the highest power of why.
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