SOLUTION: When a polynomial is divided by (x-5). The quotient Is 5x^2+3x+12 with a remainder 7. Find the polynomial.

Question 988705: When a polynomial is divided by (x-5). The quotient Is 5x^2+3x+12 with a remainder 7. Find the polynomial.
Found 2 solutions by solver91311, Boreal:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

If you divide 13 by 5 using integer division (the kind you first learned in the 3rd grade), you have a quotient of 2 and a remainder of 3. So, if you know you have a divisor of 5, a quotient of 2, and a remainder of 3, you can multiply the quotient by the divisor and add the remainder to get back to the original dividend. 5 times 2 plus 3 is 13.

Polynomial Long Division works exactly the same way. Multiply the divisor by the quotient and add the remainder to the product to find the original dividend.

John

My calculator said it, I believe it, that settles it

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
If you multiply the two factors, you get 5x^3-22x^2-3x-60. The polynomial needs a -53 so that when synthetic division is done using 5, the last term is -53+(12*5)=7
The polynomial is 5x^3-22x^2-3x-53
5/5 ;;-22;;-3;;-53
;;;5;; 3;;12; 7

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