About this video
Using the polynomial 3x^2 - 8x + 7, the video picks out the three terms, the coefficient of each term and the exponent of each term. It shows that a subtracted term carries its negative sign, and that a constant like 7 can be read as 7x^0.
You'll be able to
- identify the terms of a polynomial, including their signs.
- state the coefficient of each term, including negative coefficients.
- state the exponent of each term, including x = x^1 and a constant = constant times x^0.
Key words
- term
- One of the parts being added together in a polynomial, such as 3x^2 or -8x.
- polynomial
- An expression made of many terms added together; 'poly' means many.
- monomial
- A polynomial with only one term in it.
- coefficient
- The number multiplying the x part of a term, such as -8 in -8x.
- exponent
- The power x is raised to in a term, such as 2 in 3x^2.
- constant
- A term with no x showing, like 7, which you can think of as 7x^0.
Transcript
In the following polynomial, identify the terms along with the coefficient and exponent of each term. So the terms are just the things being added up in this polynomial. So the terms here-- let me write the terms here. The first term is 3x squared. The second term it's being added to negative 8x.
You might say, hey wait, isn't it minus 8x? And you could just view that as it's being added to negative 8x. So negative 8x is the second term. And then the third term here is 7. It's called a polynomial. Poly, it has many terms. Or you could view each term as a monomial, as a polynomial with only one term in it.
So those are the terms. Now let's think about the coefficients of each of the terms. The coefficient is what's multiplying the power of x or what's multiplying in the x part of the term. So over here, the x part is x squared. That's being multiplied by 3. So 3 is the coefficient on the first term.
On the second term, we have negative 8 multiplying x. And we want to be clear, the coefficient isn't just 8. It's a negative 8. It's negative 8 that's multiplying x. So that's the coefficient right over here. And here you might say, hey wait, nothing is multiplying x here.
I just have a 7. There is no x. 7 isn't being multiplied by x. But you can think of this as 7 being multiplied by x to the 0 because we know that x to the zeroth power is equal to 1. So we would even call this constant, the 7, this would be the coefficient on 7x to the 0.
So you could view this as a coefficient. So this is also a coefficient. So let me make it clear, these three things are coefficients. Now the last part, they want us to identify the exponent of each term. So the exponent of this first term is 2. It's being raised to the second power.
The exponent of the second term, remember, negative 8x, x is the same thing as x to the first power. So the exponent here is 1. And then on this last term, we already said, 7 is the same thing as 7x to the 0. So the exponent here on the constant term on 7 is 0.
So these things right over here, those are our exponents. And we are done.
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