Use synthetic division to divide f(x) by x - k for the given value of k. Then express f(x) in the form f(x)=(x-k)q(x)+r for the given value of k.

f(x) = -5x4 + x3 + 2x2 + 3x - 1; k = 1

the key to this problem is in recognizing that q(x) is a quotient, and r is a remainder.

Since f(x) is a higher degree polynomial than (x-k), If we divide (x-k) into f(x), we'll get a non-fractional quotient and a fractional remainder:

f(x)/(x-k) = q(x) + r/(x-k).  Multiplying both sides by (x-k), and applying a little algebra, we have

f(x) = (x-k)q(x) + r

So, all we have to do to get f(x) in the desired form is divide it by (x-k) and then multiply the result again by (x-k).  Sounds strange, right?  But that's all there is to it!  Let's give it a shot:

k= -1, so (x-k) = (x+1).

Now, we find (either with long or synthetic division) f(x)/(x+1) = (2x3+x2+x-6)/(x+1).

f(x)/(x+1) = 2x2 - x + 2 - 8/(x+1).

we can see that q(x) = 2x2-x+2, and

r/(x+1) = -8/(x+1).

Now, multiply both sides by (x+1):

f(x) = (x+1)[2x2-x+2-8/(x+1)]

=(x+1)(2x2-x+2) - (x+1)*8/(x+1).   Notice I distributed (x+1) to q(x) and r independently.

=(x+1)(2x2-x+2) - 8.

This is in the form (x-k)q(x) + r.

Step-by-step explanation:

off the internet

a. 74 degrees

step-by-step explanation:

because the lines through the side and the box in the corners shows that these are congruent triangles and since they are mirrored the 37 degrees is also mirrored so the answer is 37 * 2 which is 74.

0

step-by-step explanation:

you can not divide by 0 so 4 ÷ 0 would be 0

0 × 9999 =0

mark brainliest   : )