Determine if the given function is a polynomial function. If so, write in standard form, then state the degree and leading coefficient. f(x)=3x2+5x+2f\left(x\right)=3x^2+5x+2f(x)=3x2+5x+2

Polynomial with n = 2 , a n = 3 n=2,a_{n}=3 n = 2 , a n = 3

Determine if the given function is a polynomial function. If so, write in standard form, then state the degree and leading coefficient. f ( x ) = 3 x 2 + 5 x + 2 f\left(x\right)=3x^2+5x+2 f ( x ) = 3 x 2 + 5 x + 2

Hey everyone. In this practice problem, we want to determine if the given function is a polynomial function, and if so, write it in standard form stating both the degree and leading coefficient. And here, the function I have is f of x is equal to 3x squared plus 5x plus 2. Now I first wanna determine if this is a polynomial function. And since I only have positive whole numbers as exponents, it looks like, yes, this is a polynomial function. And you might have already recognized that it is simply a quadratic function, which we know is just a polynomial function of degree 2. Now double checking that this is written in standard form, descending order of power with all of my like terms combined, it looks like I'm good. This is already in standard form, so I don't need to rewrite anything. Now if you already recognize that it was a a quadratic function, you would already know that your degree is 2. But looking, just double checking that in that standard form, my highest power is that 2. Now for our leading coefficient, looking at that first coefficient on that first term in standard form, it is a 3. So my leading coefficient is 3. That's all for this one. I'll see you in the next one.

Determine if the given function is a polynomial function. If so, ...

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Determine if the given function is a polynomial function. If so, write in standard form, then state the degree and leading coefficient. $f\left(x\right)=3x^2+5x+2$