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Polynomial Vocabulary - Problem 1
Some of your early homework problems when you’re working with polynomials will ask you to write them in standard form and find the degree. Remember standard form means the exponents go in order decreasing from largest to smallest and the degree is the largest exponents, so let’s check it out.
Part A. Write this polynomial in standard form. Standard form means I need the biggest exponent to come first. My biggest exponent is right there, that 3, x to the third. Keep in mind that negative means negative 1 times x to the third, so I’ve got to take the negative 1 along with me. Negative x to the third and I want to decrease my other exponents 2x² 4x it’s like 4x to the first power and then take away 8, that’s like x to the zero power. So there we go. That’s in standard form.
Can you think of what the degree is for this polynomial? Keep in mind degree means the highest exponent. We don’t care about these big constant numbers, all we care about is the exponents, remember we’re looking for the degree. So the degree of this guy is 3. This is the third degree polynomial. Degree of 3, standard form third degree.
Next one let’s check it out. We want to put this into standard form meaning we have the largest exponents and then they go in decreasing order. We’re kind of lucky. These guys are already in standard form. Look at the exponents x to the 8th, x to the 5th this is like x to the 0, they’re already decreasing, so that guy is already in standard form.
Okay, but when looking for the degree keep in mind the degree means the largest exponent, so in our case the degree here will be 8, that’s an eighth degree trinomial, trinomial because it has 3 terms.
Last but not least we have this one little funny old monomial, monomial meaning there’s only one term. Even though there’s one term, we can say it’s already in standard form because the exponents are already in decreasing order. Of course they aren’t really in the exponents, unless you wanted to write this as 8x to the 0 that’s okay if it helps make sense of this, keeping in mind anything to the 0 power is 1. So I haven’t changed the value of that 8 by multiplying it by 1. That might help you to see that the degree of that monomial which is also a constant I’m trying to use lots of vocabulary here, monomial , constant, the degree of that guy is just going to be zero because I have x to the 0, It’s the exponent on my variable term. So these problems aren’t too difficult, you guys you can absolutely do them, aim for an A+ on that test.