To find the degree and leading coefficient of the polynomial function f(x)=x^(6)(6-3x^(4)-2x^(4)), you first need to understand what these terms mean.
The degree of a polynomial is the highest power of x in any term of the polynomial. And the leading coefficient is the coefficient of the term involving the highest power of the variable.
Looking at the given polynomial function, you will observe that the expression is in the product form, there is one term, which is x^(6), and the other expression is a combination of two terms (6-3x^(4)-2x^(4)). We can combine the similar terms in the second expression which gives us 6-5x^(4). When simplified, the expression becomes x^(6)(6-5x^(4)).
Now, the multiplication of the highest powers of x from both terms will give the highest power of the function. So, by multiplying power 6 (from x^(6)) and power 4 (from -5x^(4)), you get a power of 6+4=10.
But, you should notice that the x^(4) part is in a subtracted form in parentheses, so it's not actually going to increase the degree of the polynomial. Essentially, the highest standalone degree is the one for x^6.
Therefore, the degree of the given polynomial function is 6.
Next, to find the leading coefficient, you should look at the coefficient attached to the term with that highest degree. The coefficient of x^6 in the given polynomial function is clearly 1 (since there is no other number multiplying this term).
Therefore, the leading coefficient of the given polynomial function is 1.
So, for the polynomial function f(x)=x^(6)(6-3x^(4)-2x^(4)), the degree is 6 and the leading coefficient is 1.