Polynomial divided by another polynomial

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In summary, the conversation discusses dividing two polynomials and finding the value of k and a, where the remainder is equal to (x+a). The person has attempted to solve the problem but is unsure if their calculations are correct. They are seeking assistance from others to help them find the correct solution.
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pankaz712
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If the polynomial x^4-16x^2-25x+10 is divided by another polynomial x^2-2x+k, the remainder comes out to be x+a find k and a.

My approach: I tried dividing the first polynomial by the second and then equating the remainder to (x+a). It didn't work out. Are my calculations wrong or am i on the wrong track?

I would appreciate if someone could help me out.
 
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  • #2
hi pankaz712! :smile:

(try using the X2 icon just above the Reply box :wink:)

that should work …

show us your full calculations, and then we'll see what went wrong! :smile:​
 

1. What is polynomial division?

Polynomial division is a process used to divide one polynomial expression by another polynomial expression. It is similar to long division in arithmetic, but instead of dividing numbers, we are dividing algebraic expressions.

2. What is the purpose of polynomial division?

The purpose of polynomial division is to simplify and break down complex polynomial expressions into smaller, more manageable ones. This allows us to solve equations, find roots, and factor polynomials more easily.

3. How is polynomial division performed?

To divide one polynomial by another, we use the steps of long division. First, we identify the highest degree term in the dividend and divide it by the highest degree term in the divisor. This gives us the first term of the quotient. Then, we multiply the divisor by this term and subtract it from the dividend. The resulting expression becomes the new dividend, and the process is repeated until there is no remainder.

4. Can any polynomial be divided by another polynomial?

Yes, any polynomial can be divided by another polynomial. However, the resulting quotient may not always be a polynomial. In some cases, it may be a rational expression or a polynomial with fractional coefficients.

5. What is the remainder in polynomial division?

The remainder in polynomial division is the expression that is left over after the division process is complete. It is the part of the dividend that could not be divided evenly by the divisor. In some cases, the remainder may be zero, indicating that the division was completed without any remaining terms.

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