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Let f(x)=x^n+a_(n-1)x^(n-1)+...+a_0 with n>=2 and a_i an integer have a rational root x=p/q.

Consider q^(n-1)f(p/q).

q^(n-1)f(p/q)=p^n/q+a_(n-1)p^(n-1)+...+a_0q^(n-1)=0

==> a_(n...

tanx = sinx/cosx. Express this as: sinx*(cosx)^-1. Remembering the product rule: "y = f(x)g(x), dy/dx = f'(x)g(x) + f(x)g'(x)". sinx differentiates to cosx and cosx differentiates to -sinx. Also...

Writing a personal statement for any course is a daunting task and when the course you're applying for has a 10 people applying for every 1 place, it can at times seem impossible. As a current medical stu...

Chlorine, Cl, and Florine, F are both in group 7 of the periodic table so they have 7 electrons in the outer energy level, called valence electrons. Each fluorine atom makes one covalent bond to the chlor...

This is a handy trick for quadratic equations ax^2 + bx + c = 0.

e.g. (x^2 + 5x + 6). So a = 1, b = 5 and c = 6.

To complete the square, let x^2 + 5x + 6 = 0. Then, take 6 to the other side ...