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Evaluate each polynomial for $a=-2$ and $b=3 .$ S…

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Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Problem 6 Problem 7 Problem 8 Problem 9 Problem 10 Problem 11 Problem 12 Problem 13 Problem 14 Problem 15 Problem 16 Problem 17 Problem 18 Problem 19 Problem 20 Problem 21 Problem 22 Problem 23 Problem 24 Problem 25 Problem 26 Problem 27 Problem 28 Problem 29 Problem 30 Problem 31 Problem 32 Problem 33 Problem 34 Problem 35 Problem 36 Problem 37 Problem 38 Problem 39 Problem 40 Problem 41 Problem 42 Problem 43 Problem 44 Problem 45 Problem 46 Problem 47 Problem 48 Problem 49 Problem 50 Problem 51 Problem 52 Problem 53 Problem 54 Problem 55 Problem 56 Problem 57 Problem 58 Problem 59 Problem 60 Problem 61 Problem 62 Problem 63 Problem 64 Problem 65 Problem 66 Problem 67 Problem 68 Problem 69 Problem 70 Problem 71 Problem 72 Problem 73 Problem 74 Problem 75 Problem 76 Problem 77 Problem 78 Problem 79 Problem 80 Problem 81 Problem 82 Problem 83 Problem 84 Problem 85 Problem 86 Problem 87 Problem 88 Problem 89 Problem 90 Problem 91 Problem 92 Problem 93 Problem 94 Problem 95 Problem 96 Problem 97 Problem 98 Problem 99 Problem 100

Problem 60 Hard Difficulty

Evaluate each expression. See Example 2 and $3 .$
$-y^{4}+y^{3}+y^{2}+y+1$
for
a. $y=1$
b. $y=-1$

Answer

a. 4
b. -2

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Elementary and Intermediate Algebra

Chapter 5

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Section 4

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Video Transcript

Okay, here we have a polynomial expression and we're going to evaluate it for y equals one. And what that means is we're going to substitute one in for why Everywhere we have a why and then we simplify. So we have the opposite of one to the fourth plus one cubed plus one squared, plus one plus one. So one of the fourth is one. The opposite of that would be negative. One noticed the opposite is after raising to the fourth one. Cubed is once we have a +11 squared is one another plus one and then the two plus ones at the end. Add all that up and you get three. Now we're going to evaluate it for y equals negative one. So the same idea. But you're substituting negative one in for Why so the opposite of negative one to the fourth plus negative one cubed plus negative one squared plus negative one plus one. And it really does help to have all those parentheses around the negative ones to give the order of operations straight. Okay, so we're going to raise negative one to the fourth. That gives us positive one, but it's multiplied by a negative negative. 12 The third is negative one. So we have negative what? We have minus one there. Negative one squared is positive ones. We've plus one there. Plus negative one is the same. It's minus one. And then at the end, we have our plus one. So what does this add up to With three negative ones and two positive ones, So that's gonna add up to negative one.

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Alan S. Tussy, R. David Gustafson

Elementary and Intermediate Algebra

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