This week we didn’t learn very much that was new but we were introduced to a new unit called solving quadratic equations. We focused on factoring just like we did last year in grade 10 math. It was mostly review and fairly easy to pick up again, but we did learn some new skills to solve harder or “uglier” equations.

Ex : pg181 #16a

$(7x-5)^2$$8(7x-5)$ + $15$

When doing this question, we learned that we need to find something common within the equation which in this case is $(7x-5)$

We replaced that with any variable, I chose x. This gives us $x^2 - 8 + 15$ (the pattern we want to see)

After we factor this out like we normally do finding the sum of b, product of c : $(x - 3)(x - 5)$

When that is done we plug in the x to the equations and will result to our final answer : $(7x-5-3)(7x-5-5)$

Answer : $(7x-8)(7x-10)$

What I learned this week is that it’s very easy to miss clues to find the answer of the equations, but if we pay attention to previous things we already know, it is always possible to solve the equations. We also learned an acronym for the steps of factoring : CDPEU.

Common (find the greatest common factor)

Difference (are there any difference of squares?)

Pattern ( $x^2 + x - 1$ )

Easy ^

Ugly (a number in front of the $x^2$)

Nothing much was presented this week but we will learn more in the upcoming weeks.