Main content

## Algebra (all content)

# The parts of polynomial expressions

CCSS.Math: ,

Learn about the parts of polynomial expressions (including terms, coefficients, and exponents). Created by Sal Khan and Monterey Institute for Technology and Education.

## Video 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.