Two algebra questions! ! 1) divide 8x4 – 6x3 + 7x2 – 11x +10 by 2x – 1 using long division. show all work. then explain if 2x – 1 is a factor of the dividend. 2) factor f(x) = x4 + x3 – 8x2 + 6x + 36 completely. show all work for finding the factors. sketch the graph by hand, use the graph below, label at least 6 points on the graph. state the factors and the roots. (hint: two of your factors will be complex

ANSWER TO QUESTION 1

Check attachment for long division.

From our long division we can write the following;

Since the polynomial

leaves a non zero  remainder of when divided by , we conclude that not a factor of the dividend,

ANSWER TO QUESTION 2

We want to factor

The possible rational roots are;

We found

and

.

This means that and are factors of the polynomial.

This also means that

is also a factor of the polynomial

So we apply long division to obtain the remaining factors as shown in the attachment.

We factor further to obtain;

(hint): the answer is in the question.