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

1. 3. can also be expressed as (22/7)

2. -4.5

3. 3.6

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step-by-step explanation: