Calculus Midoriさんのイラストまとめ

>Andddd for the final example so we can actually start this lesson: x^2+15x+56
>a=1, b=15, c=56
>+ c, both factors will share bx's, 15x, sign, +.
>(x+8)(x+7)

>x^2+3x-18
>a=1, b=3, c=-18
>- c, bigger factor will take bx's, 3x, sign, which is +.
>(x+6)(x-3). The larger factor, 6, took the +, while 3 gets the -.

>x^2-9x+20
>a=1, b=-9, c=20
>Since it is + c, that means both factors will have the same sign as bx, -9x, which is -.
>If we look at its factored form... (x-4)(x-5), see how both factors are both -?

>Let's entertain a few examples.
>I have created a list of very nice quadratics in their standard and factored forms. I'll go through each of them one by one.

>- c means that both factors will have different signs, with the larger factor taking the sign of bx.
>+ c means that both factors will share the same sign, specifically with the sign of bx.
>Sounds confusing? I'll clarify later. Stay patient like you've been for 2 months.

>I'll use this format: ax^2 + bx + c = 0, where a, b, and c are constants. This is the standard or canonical form of quadratics.
>In order to interpret, we have to look at the signs of bx and c.

>It ends up looking a little like this. Nice and condensed! Just like Ryoko.
>We can now start interpreting the expression's implications about its factors.

>Here's an easy one. It's a little convoluted, but I want to make the first step crystal clear!
>You combine your like terms, first thing. Like terms share the same variable and power.
>5x and -6x both share the same variable, x, and same power, 1. The coefficient doesn't matter.

>Most notably, a form where the zeros are easily readable. I'll be covering 4 methods here, they're all you'll need to know for now: Grouping, special cases, long division, and synthetic division.
>I'll try to cover these one by one.

UNIT 1: FACTORING P.1

>Due to poll results requesting for a factoring review, we'll be momentarily stopping our limits and continuity to do this quick mini lesson.
>As you know, factoring is simplifying the expression into a more useful form.