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Current time:0:00Total duration:2:36

The parts of polynomial expressions

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 can just do that is it's being added to negative 8x so negative 8x is the second term and then the third term here is seven 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 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 its 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 this 7 this would be the coefficient on 7 X to the 0 so you could view this you could view this as a coefficient so this is also a coefficient so let me make it clear these three things are coefficients 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 8 X X is the same thing as X to the first power so the exponent here is one and then on this last term we already said this is seven is the same thing as seven X to the zero so the exponent here on the constant term on seven is zero so these are these things right over here those are our exponents exponents and we are done