# Given #f(x) = -7x^2(2x-3)(x^2+1)# how do you determine the following?

##
**a)** The degree of #f(x)# .

**b)** The leading coefficient.

**c)** The maximum possible number of turning points.

**d)** The real zeros of #f(x)# .

**e)** The end behaviour of #f(x)# as #x->-oo#

**f)** The end behaviour of #f(x)# as #x->oo#

**a)** The degree of

**b)** The leading coefficient.

**c)** The maximum possible number of turning points.

**d)** The real zeros of

**e)** The end behaviour of

**f)** The end behaviour of

##### 1 Answer

**a)**

**b)**

**c)**

**d)**

**e)**

**f)**

#### Explanation:

Given:

#f(x) = -7x^2(2x-3)(x^2+1)#

It is not too arduous to multiply out

In particular, note that the term of highest degree in

#-7x^2(2x)(x^2) = -14x^5#

**a)** The degree of *quintic*.

**b)** The leading coefficient is the coefficient of this term, namely

**c)** A polynomial of degree

**d)** The real zeros of a polynomial correspond to its linear factors. In our example

**e)** As

**f)** As

graph{-7x^2(2x-3)(x^2+1) [-5, 5, -25, 25]}