Recent content by bwpbruce

I'm just glad you guys are still here.

Thanks for pointing this out seven years later.

Is this the correct symbol to use for average rate of change: \overline{\triangle}=\dfrac{f(b)-f(a)}{b-a}

Was aware of this resource, but was looking for more of a book resource.

What is the best resource for learning how to do problems that ask you to "Show that this is true" or Prove that is this is true"?

You're still asking about $b=\pm\dfrac{1}{2}$?.

Which of my expressions are you implying is something other than closed form?

$x^3 - 9x -440$ $=x^3 - 8x^2 + 8x^2 - 64x + 55x - 440$ $=x^2(x - 8) + 8x(x - 8) + 55(x - 8)$ $=(x - 8)(x^2 + 8x + 55)$ $=(x - 8)(x^2 + 8x + 16 -16 + 55)$ $=(x - 8)((x + 4)^2 + 39)$ $=(x - 8)(x + 4)^2 - (-39))$ $=(x - 8)(x + 4)^2 - (\sqrt{39}i)^2$ $=(x - 8)(x + 4 - \sqrt{39}i)(x + 4 + \sqrt{39}i)$

Complete The Square Method: $x^2 + 4x - 1 $ $= x^2 + 4x + 4 - 4 - 1$ $ = (x + 2)^2 - 5$ $ = (x + 2)^2 - (\sqrt{5})^2$ $ = (x + 2 + \sqrt{5})(x + 2 - \sqrt{5})$

Is there not a distinction between factoring a polynomial EXPRESSION and finding the roots of a polynomial EQUATION? Furthermore, even if we were tasked with finding roots, in accordance with the zero product property, $b=\pm\dfrac{1}{2}$ would be $\textit{possible}$ roots. But it is clear that...

$\dfrac{2}{3}b^5 - \dfrac{1}{6}b^3+\dfrac{4}{9}b^2 - 1$ $=\dfrac{12}{18}b^5 - \dfrac{3}{18}b^3 + \dfrac{8}{18}b^2 - \dfrac{18}{18}$ $=\dfrac{1}{18}\left(12b^5 - 3b^3 + 8b^2 - 18\right)$ $=\dfrac{1}{18}\left(3b^3(4b^2-1)+2(4b^2-9)\right)$ $=\dfrac{1}{18}\left(3b^3(4b^2-1)+2\left(4b^2-9...

Just some questions about Linear Equations, Linear Combinations, and the Zero Vector. I prefer if we discuss it in chat. This forum setup isn't ideal for me.

I was wondering if there was anyone comfortable enough about basic to advanced linear algebra concepts who would be willing to participate in a chat/whiteboard based platform to discuss or answer questions concerning such concepts. I need clarification on a few things

The no indent command doesn't seem to work well in conjunction with the align command. - - - Updated - - - If you can show me a way to post the text so that it is not indented but still align the equal signs, then that's what I want to be able to do.

If I use the align command, my text is usually either indented or centered by default. What do I need to do in order for my text to align left. I prefer if someone demonstrate how to do it.\begin{align*}\dfrac{a}{t} - \dfrac{b}{t}&=\dfrac{1}{t}(a) - \dfrac{1}{t}(b) \\&=\dfrac{1}{t}(a - b)...