Recent content by SwimmingGoat

aha! Thank you! I knew I was missing an obvious place to start. This is what happens when I do math for three hours straight...

Ok, I've been working on a long problem (if you want all the steps I've taken to get to this point, I'll give them to you, but they aren't relevant, and I've done them correctly), and now I'm slightly stuck. Right now I have f(x)=\frac{x^2+2x}{2x+2}. The current problem asks me if the graph...

Whoops! Thanks for catching that.

Thank you so much for your help! For the second one, I applied your idea with the fact that a^3+b^3=(a+b)(a^2-ab-b^2). I let a=1and b=\sqrt[3]{2}.

Ok, now I have expanded it out as you suggested: p(x)=(ax^2+bx+c)(x^2-14\sqrt{2}x+87) which ends up with: p(x)=(a)x^4+(b-14\sqrt{2}a)x^3+(87a-14\sqrt{2}b+c)x^2+(87b-14\sqrt{2}c)x+87c From here, do I try to make educated guesses for a,b, and c? Or do these restrictions give some obvious...

Problem: q(x)=x^2-14\sqrt{2}x+87. Find 4th degree polynomial p(x) with integer coefficients whose roots include the roots of q(x). What are the other two roots of p(x)? I found that the two roots of q(x) are x=7\sqrt{2}-\sqrt{11} and x=7\sqrt{2}+\sqrt{11}. Since they are conjugates of...

Here's my problems: How might you "rationalize the denominator" if the expression is \frac{1}{2+7√2+5√3} or \frac{1}{\sqrt[3]{2}+1}? I know that in typical problems where we rationalize the denominator, we simply have to multiply the denominator and numerator by the conjugate of the denominator...