math
posted by jezebel .
Each divisor was divided into another polynomial , resulting in the given quotient and remainder. Find the other polynomial the dividend
Divisor: x+10,quotient,x^26x+10,remainder :1
I am so confused help is appreciated

I think what you're being asked is this. There's some polynomial  let's call it f(x)  that when divided by (x + 10) equals (x^2  6x + 10) with remainder 1. What is f(x)?
If I'm right, then we should be able to find it by multiplying (x^2  6x + 10) by (x + 10), and then adding 1 to the result. Let's do that:
To multiply (x^2  6x + 10) by (x + 10), multiply (x^2  6x + 10) by x, then multiply (x^2  6x + 10) by 10, and add the two together. That is:
The product of (x^2  6x + 10) and x is (x^3  6x^2 + 10x).
The product of (x^2  6x + 10) and 10 is (10x^2  60x + 100).
The sum of the above two expressions is (x^3 + 4x^2  50x + 100). Now add that 1 to it to allow for the remainder you were told about earlier: that gives (x^3 + 4x^2  50x + 99).
I think that's the answer, so now let's check it. If I'm right, then (x^3 + 4x^2  50x + 99) divided by (x + 10) should equal (x^2  6x + 10) with remainder 1. Does it?
To divide (x + 10) into (x^3 + 4x^2  50x + 99), ask what is x^3 divided by x? The answer is x^2, so that's the first (squared) term of my quotient. Next, multiply (x + 10) by x^2 and subtract the result from (x^3 + 4x^2  50x + 99), just as you would when doing the first step of a long division sum:
(x^3 + 4x^2  50x + 99) minus (x^3 + 10x^2) equals (6x^2  50x + 99).
To divide (6x^2  50x + 99) by (x + 10), ask what is 6x^2 divided by x? The answer is 6x, which is the second (linear) term of my quotient. Next, multiply (x + 10) by 6x and subtract the result from (6x^2  50x + 99), again just as you would when doing the second step of a long division sum:
(6x^2  50x + 99) minus (6x^2  60x) equals (10x + 99).
Finally, (10x + 99) is 10 times (x + 10) remainder 1. So 10 is the third (constant) term of my quotient. So the complete answer is the first (squared) term of my quotient plus the second (linear) term of my quotient plus the third (constant) term of my quotient, which is (x^2  6x + 10) remainder 1. So I think I've got it right.
Does that help? It would be easier to express the above if I could write it out like a proper long division sum, but I'm hoping you can relate the above to the examples you'll have seen in your class, which will probably have been written out this way.
Respond to this Question
Similar Questions

PreCalc
Fill in the blank; •In the process of polynomial division (Divisor)(Quotient)+_______=_______ •When a polynomial function f is divided by xc, the remainder is _______. •If a function f, whose domain is all real numbers, is even … 
Mathhelp help help
1)when a certain polynomial is divided by x  3, the quotient is x^2+2x5 and the remainder is 3. what is the polynomial 2) Find each quotient and remainder. Assume the divisor is not equal to zero. a)(2x^2+29xx^340)/(3+x) b)(6+7x11x^22x^3)/(x+9) … 
Mathhelpppppp
1)when a certain polynomial is divided by x  3, the quotient is x^2+2x5 and the remainder is 3. what is the polynomial 2) Find each quotient and remainder. Assume the divisor is not equal to zero. a)(2x^2+29xx^340)/(3+x) b)(6+7x11x^22x^3)/(x+9) … 
math/algebra
Find the quotient and remainder when the dividend is 262 and the divisor is 11. Please show work 
math/algebra
Please show work Find the quotient and remainder when the dividend is 262 and the divisor is 11. 
math
Each dividend was divided by another polynomial, resulting in the given quotient and remainder. Find the divisor Divided:5x^3+x^2+3 ,quotient:5x^214x+42, remainder:123 
Algebra
When a polynomial is divided by x+3, the quotient is x^3+x^24 and the remainder is 8. Find the dividend? 
Algebra
When a polynomial is divided by x+3, the quotient is x^3+x^24 and the remainder is 8. Find the dividend? 
Math
The quotient equals the divisor, then the dividend equals the (A) square root of the divisor (B) divisor (C) divisor^2 (D) quotient 
math
Use polynomial long division to find the quotient and the remainder when 2x 3 +x 2 +3x−1 is divided by x+4 . Also, check your answer by showing that 2x 3 +x 2 +3x−1 is equal to x+4 times the quotient, plus the remainder. …