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Find a three-term polynomial of degree 2 whose value will be 1 when it is evaluated for $x=2$

$2 x^{2}-3 x-1$

Algebra

Chapter 5

Exponents and Polynomials

Section 4

Polynomials

Campbell University

McMaster University

Idaho State University

Lectures

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Find the degree of each po…

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02:33

Find a polynomial of degre…

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01:36

01:01

Find the value of each pol…

00:59

00:46

02:08

00:23

Identify the degree of the…

00:13

00:32

Write an equation for the …

01:12

Find a polynomial function…

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02:22

State the degree of each p…

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Okay, This is an interesting problem to think about. So we're creating our own three term polynomial. So we have something plus something plus something. Three terms. The degree is, too. That means the highest exponents will be, too. And when we plug in X equals two into it, we should get one for the value of the whole expression. So I think a good way to start would just be to make up whatever we want for the 1st 2 terms and then start evaluating it with a two in it and see what we have to add to make it equal one. So I'm going to keep it simple. I'm going to start with X squared and X. Now we have our degree to polynomial as long as the third term does not have a degree higher than too. In fact, we're gonna have to make the third term a constant, which makes it pretty simple, actually, because it's whatever constant we're going to need to make it work out to be a one. So now let's go ahead and substitute to In here we have two squared plus two plus something, and we want this all to work out to be one. So two squared is four plus two. Plus something is going to be one. So four into a 606 plus something is going to be one. Well, that's going to have to be negative. Five. So back in the beginning, if we make that a negative five there we have our three term polynomial of degree to which, when evaluated for two, will give us one.

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