# Polynomial Function - Concept

A polynomial function is a function comprised of more than one power function where the coefficients are assumed to not equal zero. The term with the highest degree of the variable in **polynomial functions** is called the leading term. All subsequent terms in a polynomial function have exponents that decrease in value by one.

So polynomial functions, polynomials are just functions like anything else. So anytime you see f of x or g of x, p of x anything like that you're just saying you're dealing with a function. So how we deal with them is just like we would any other functions, if I asked you to do f of 5 you simply plug in 5 into f and see what you come up with. So plug in 5 in we end up with 5 squared minus 7 times 5 plus 2, just remember whenever you see an x you plug in 5. This turns out to be 25 minus 35 plus 2, negative 10 plus 2 is negative 8. Polynomial function plug it in.

Over here we're going to look at a different function g of x, g of x is a linear function and this time we're asking for g of x minus 2. So before we just plugged in a simple number wherever we saw x we plugged in, what was it 5, now we're going to plug in x minus 2. Same exact idea but little twist just because we have something else plugging I x minus 2 we end up with 8 and then our x just becomes x minus 2 minus 4. Okay if we can simplify this up this just turned into 8x minus 16 minus 4 combining like terms leaves us with 8x minus 20. So g of x minus 2 isn't a number like we had over here but it's still our answer just still having another x.

The polynomial of functions in a lot of way behave like anything else weÂ’ve seen just plug them in and see what comes out.

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