Note: There is a strong possibility of extremely sloppy weather tonight into tomorrow morning. Plan for extra travel time!
Test 4 is scheduled for tomorrow, Monday 2 December 2019, at our usual time. There will be assigned seating as there was for Test 3, but not the same seating, so try to arrive a bit early.
Some people in the class seem to think that they are only required to show up on Test days. This is false. Now would be an excellent time to review my Course Policies.
I strongly recommend that you read the post that I wrote up on the example I did in class of what NOT to do when solving a rational equation.
Something I should have mentioned there but forgot: Whenever you solve any type of equation, it is important NOT to divide out or “cancel” any factor which contains a variable (and so could possibly be equal to 0). If you do this you risk losing a solution to the equation!
For example, here is a thing I have witnessed: in trying to solve
$5x^{2} = 3x$
one person thought to divide both sides by $x$: (WRONG!)
$\frac{5x^{2}}{x} = \frac{3x}{x}$
$5x = 3$
$x = \frac{3}{5}$
This certainly is a solution of the original equation, as you can see by substituting it back in: the problem is that there is another solution, namely $x = 0$, which we lost when we divided out that factor. This being a quadratic equation, a safe way to solve it is to use the Zero Product Property:
$5x^{2} = 3x$
$5x^{2} – 3x = 0$
$x(5x – 3) = 0$
$x = 0$ or $5x – 3 = 0 \implies x = \frac{3}{5}$
In any case, avoid at all costs dividing both sides of any equation by an expression which might possibly be 0.
I also strongly recommend that you read these typed up solutions for the Quiz last Thursday, which show how to make sure you are using the relevant patterns.
MAT1275coQuiz-27Nov2019-answers
Make sure that you understand and use the important patterns: extra credit will be given to those who correctly use these patterns when they are appropriate!
• Product of conjugates (Difference of Squares)
$(A + B)(A-B) = A^{2} – B^{2}$
• Perfect square trinomial (Square of a binomial):
$(A + B)^{2} = A^{2} + 2AB + B^{2}$
$(A – B)^{2} = A^{2} – 2AB + B^{2}$
If you happen to recall that $(a + bi)(a-bi) = a^{2} + b^{2}$ you can make the solution to problem #3 on the Quiz a bit shorter, but make sure that you do it correctly in any case!
Also, the Definition of square root: $\left(\sqrt{A}\right)^{2} = A$
I will refer you again to the advice and resources I have posted for the previous 3 tests: remember that there are video resources available for all our topics!
