# Tagged Questions

35 views

### Write equation as a multinomial in the variables x and Sin[y] and extract the coeficient of x*Sin[y]^2 [closed]

I need help solving this problem. Thank you. (a*x^2 + b*x*Sin[y] + c*Sin[y])^2 + (a*Sin[y]^2 + b*x)^3 Write the above as a multinomial in the variables x and Sin[y] and extract the coeficient of ...
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### How can Mathematica help me to find a real radical expression for roots of this polynomial?‎

The polynomial P(x)=x^‎‏4‏‎-‎‏4‏x^‎‏2‏‎-‎‏2‏x+‎‏1‏‎ has ‎‏4‏‎ real roots (this can be clearly checked by plotting). But solving ...
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### HornerForm of polynomials in terms of E^(i x)

I want to know how to get the HornerForm of the following expression in terms of E^(I x): ...
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### How to find monotonically increasing intervals of a function

I tried this code, but not working Clear[f]; f[x_] := x^3 - 3 x + 2; ForAll[{x1, x2}, x1 < x2, f[x1] < f[x2]] Reduce[%, {x1, x2}, Reals] I expected the ...
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### Is there a way to speed up Simplify and/or PolynomialReduce Modulus-> 2?

I'm trying to simplify a series of equations with at most 64 input terms. As the number of terms involved in the equations increase, the runtime seems to grow exponentially. Does anyone know of ways ...
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### How can I prevent a polynomial from being simplified?

I'm having a problem with polynomials. Let's say I have a polynomial "2x^2 - 5x + 6 - 3x^2" .. How can I check that this expression is not simplified ? Additionally, I would like to locate the ...
374 views

### How to deduce a generator formula for a polynomial sequence?

Consider a polynomial sequence $\{p_n\}$ generated by some (simple) rule:  \begin{array}{l} p_1(x)=x \\ p_2(x)=2 x-x^2 \\ p_3(x)= x^3-3 x^2+3 x \\ p_4(x)=-x^4+4 x^3-6 x^2+4 x \\ p_5(x)= x^5-5 ...