Simple question regarding polynomials

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So if k != 0, then k(x-1) = P(y) != 0. So, k must equal 0?In summary, the conversation discusses the relationship between a polynomial k in x and y and a polynomial q in y, where k(x-1) = q. The question is whether k must be equal to 0. It is noted that if k=0, then k(x-1)=q=0, and if k != 0, then k(x-1) = P(y) != 0. Therefore, it is concluded that k must equal 0 in order for the equation to hold true.
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slevvio
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Hello all I had a simple question that I am intuitively sure I know the answer to but can't quite prove it.

Suppose k is a polynomial in x and y, and k(x-1) = q for q some polynomial in y. Then is k = 0 ?

How do I verify that k must be equal to 0? I can see that to just get a polynomial in y we have to try to get rid of that x term, but I can't quite prove why we can't just make some polynomial that gets rid of it somehow.

any help would be appreciated, thanks
 
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Suppose k != 0, so q = ...
 
  • #3
If k=0, then k(x-1)=q=0.

If you let a polynomial in y be P(y) then if k=P(y)/(x-1), q=P(y)...
 

1. What is a polynomial?

A polynomial is a mathematical expression that consists of variables and coefficients, usually combined through addition, subtraction, and multiplication. It can also contain exponents, but not division or square roots.

2. How do you simplify a polynomial?

To simplify a polynomial, you need to combine like terms by adding or subtracting their coefficients. You can also use the distributive property to remove parentheses and combine like terms. The goal is to end up with a polynomial in its simplest form, with no like terms that can be further combined.

3. What is the degree of a polynomial?

The degree of a polynomial is the highest exponent value of the variable in the expression. For example, in the polynomial 3x^2 + 5x + 2, the degree is 2 because that is the highest exponent value of x.

4. What is the difference between a monomial, binomial, and trinomial?

A monomial is a polynomial with only one term, such as 5x or 2y^4. A binomial has two terms, and a trinomial has three terms. For example, 3x^2 + 5x is a binomial, and 2x^3 + 4x^2 + 6x is a trinomial.

5. What are the different types of polynomials?

The different types of polynomials include monomials, binomials, trinomials, and higher degree polynomials. There are also special types of polynomials, such as quadratic polynomials (degree of 2) and cubic polynomials (degree of 3). Polynomials can also be classified by their number of terms, such as a monic polynomial (leading coefficient of 1) or a constant polynomial (no variable terms).

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