Question

when a polynomial is divided by x-4, the quotient is x^2-5x+4+1/x+4. what is the polynomial?

Answer 1

i think
multiply (x-4) by (x^2-5x+4+1)

and just add on the x+4

so

(x-4)*(x^2-5x+4+1) + x+4

Answer 2

could be wrong

Answer 3

Let y = unknown polynomial
Then y/(x+4) = x^2-5x+4 + 1/(x+4)
Multiply both sides by (x+4) to solve for y

Answer 4

i suck at this.

Answer 5

Or do something close to what @timo86m did (small adjustment)
(x-4)*(x^2-5x+4) + 1

Answer 6

This follows the pattern
polynomial = divisior * quotient + remainder

Answer 7

so would the answer be 20x^4-15?

Answer 8

That's not what I got. Let me check my work.

Answer 9

Question: In the problem:
\[ \large x^2-5x+4+\frac{1}{x+4}\]

Is the remainder over x+4 or x-4. If your dividing by x-4, the denominator should be x-4 as well. Would you check that for me?

Answer 10

it's over x-4 sorry

Answer 11

Cool.

Answer 12

so my answer wasn't right ?

Answer 13

I got something different.

Answer 14

so the remainder is -15?

Answer 15

The "remainder" is the 1 that was originally divided by x-4.

Answer 16

ok so i don't have to put that then i just have to x^3-9x^2+24x-15

Answer 17

Yep. And it checks out. Just divide the polynomial you found by x-4.

Answer 18

so my ploynomiial is x^3-9x^2+24-15 or x^2-5x+4??

Answer 19

polynomial = x^3-9x^2+24x-15

divisor = x - 4
quotient = x^2-5x+4
remainder = 1

Answer 20

can i ask u another one?

Answer 21

Sure, post a new question. I'll look for you.