Question

PLEASE HELP PRECALC!! 1. Is the function f(x)=5x^2-3x^4+3/4x-7 a polynomial function? If so, state its degree and the leading coefficient. A. The function is not a polynomial B. The function is a polynomial. The degree is 2 and the leading coefficient is 5 C. The function is a polynomial. The degree is 4 and he leading coefficient is -3. D. The function is a polynomial. The degree is 4 and the leading coefficient is 5.

Answer 1

Answer:

No, not a poly. fn.

Step-by-step explanation:

Because of the division by (4x - 7), the given function is NOT polynomial.

Answer 2

Answer:

Step-by-step explanation:

If we put this polynomial (yes it is a polynomial) in order of descending powers of x, it would be

$f(x)=-3x^4+5x^2+\frac{3}{4}x-7$

The definition of a polynomial is an expression of more than 2 algebraic terms, especially the sum of several terms that contain different powers of the same variable(s).

Not just a sum.  A difference too, but since every subtraction problem can be written as an addition, that's why they say "the sum of several terms".  The degree of the polynomial is the same as the highest power of x.  Ours is a 4th degree.  The leading coefficient is the first number that leads the polynomial when it is put into order of descending powers of x.  Our coefficient is -3.  To sum up:

Yes, it is a polynomial; it is a degree 4 with a leading coefficient of -3

That is choice C