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Polynomial Function - Concept

Teacher/Instructor Carl Horowitz
Carl Horowitz

University of Michigan
Runs his own tutoring company

Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!

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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