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;

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.

h= 12 inches

step-by-step explanation: