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bergausstein
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how do you write a polynomial in three variables say x,y,z in standard form?
MHB How to Write a Polynomial in Standard Form with Three Variables?
- Thread starter bergausstein
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- Form Polynomials Standard
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To write a polynomial in standard form with three variables x, y, and z, it is essential to arrange the terms in descending order of their total degree. The standard form can be expressed as P(x,y,z) = a_n (xyz)^n + a_{n-1}(xyz)^{n-1} + ... + a_1 xyz + a_0, where each term is a product of coefficients and variables raised to non-negative integer powers. The coefficients a_n, a_{n-1}, ..., a_0 are real or complex numbers. Clarity in the arrangement of terms is crucial for proper interpretation and manipulation of the polynomial. Understanding this structure is fundamental for working with polynomials in multiple variables.
For the sake of argument, lets assume this is, in fact, a right triangle with a rectangle inscribed in it.
Here is what looks like a very elegant solution:
Triangles A and B are similar
a/4=2/b
ab=8
But what is happening in that second line? Is there a property of similar triangles I'm forgetting?
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