Factor f(x)=x4-x3-7x2+13x-6 completely. then sketch the graph

ANSWER TO QUESTION 1

.

EXPLANATION

The function given to us is,

According to rational roots theorem,

are possible rational zeros of  

.

We find out that,

Also

This implies that  

are factors of

and hence is also a factor.

We perform the long division as shown in the diagram.

Hence,

.

ANSWER TO QUESTION 2

Sketching the graph

We can see from the factorization that the roots  

and have a multiplicity of 1, which is odd. This means that the graph crosses the x-axis at this intercepts.

Also the root has a multiplicity of 2, which is even. This means the graph does not cross the x-axis at this intercept.

Now we determine the position of the graph on the following intervals,

We can now use these information to sketch the function as shown in diagram

a is the correct

2nd one in the first row is correct