From 94f1730bb296c77856b2fbdb80826c5056abbe84 Mon Sep 17 00:00:00 2001 From: eggy Date: Mon, 26 Sep 2022 11:13:05 -0400 Subject: [PATCH] math117: fix pfd directions --- docs/ce1/math117.md | 9 +++++---- 1 file changed, 5 insertions(+), 4 deletions(-) diff --git a/docs/ce1/math117.md b/docs/ce1/math117.md index 3a4fba4..23610c2 100644 --- a/docs/ce1/math117.md +++ b/docs/ce1/math117.md @@ -170,12 +170,13 @@ Please see [SL Physics 1#6.1 - Circular motion](/g11/sph3u7/#61-circular-motion) In order to PFD: -1. Factor the denominator into irreducibly quadratic or linear terms. +1. Factor the denominator into *irreducibly* quadratic or linear terms. 2. For each factor, create a term. Where capital letters below are constants: - A linear factor $Bx+C$ has a term $\frac{A}{Bx+C}$. - - A quadratic factor $Dx^2+Ex+G$ has a term $\frac{H}{Dx^2+Ex+G}$. -3. Set the two equal to each other such that the denominators can be factored out. -4. Create systems of equations to solve for each constant. + - An *irreducibly* quadratic factor $Dx^2+Ex+G$ has a term $\frac{Hx+J}{Dx^2+Ex+G}$. + - Duplicate factors have terms with denominators with that factor to the power of 1 up to the number of times the factor is present in the original. +4. Set the two equal to each other such that the denominators can be factored out. +5. Create systems of equations to solve for each constant. !!! example To decompose $\frac{x}{(x+1)(x^2+x+1)}$: