8/18/2019 Mathematics - Formulas and Tips

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POLYNOMIALS

Synthetic Division- Write down all coefcients ONLY (ignore sign) or eachpower, leaving 0 or missing powers- Bring down the rst term to the !ottom- "#ltipl$ it !$ the coefcient $o#%re dividing (&ero othe #nction) (e'g' -, *''''' *,-)- +#t it !elow the net coefcient and add them down- "#ltipl$ it !$ the coefcient $o#%re dividing andrepeat

Factor Theorem $o# inp#t the &ero o a #nction into the e.#ation

and it%s e.#al to &ero, then that #nction is a factor o that e.#ation/

Remainder Theorem $o# inp#t the &ero o the dividing #nction into thedivided e.#ation and get a n#m!er, then that n#m!er

is the remainder o the .#otient/

BINOMIALS

Coecient of ne!t term"

C =coefficient of previous∗exponent of previous x

exponent of previous y  + 1

rth term of #! $ y%n"

rth

term=  n !

(n−r+1)! (r−1)! x

n−1+1 y

r−1

S&m of coecients of an e!'ansion"

- #!stit#te 1 or each varia!le and e.#ate

()ADRATIC FORM)LA

(&adratic Form&*a"

 x=−B ±√ B2−4 AC 

2 A

Discriminant and Pro'erties"

B2−4  AC 

2 0, roots are e.#al 31, roots are real 4 #ne.#al

51, roots are imaginar$

Pro'erties of +&adratic roots"

∑ of Roots , x1+ x

2=−B A

 Product of Roots , x1 x2=

C 

 A

PARTIAL FRACTIONS

Brea,in- do.n a 'o*ynomia*s

- +#t each e.#ation as a denominator- powered, each power is a denominator (e'g'(*1)6 then (*1)1, (*1)7, (*1)6 are separatedenominators)- 8 varia!le goes in the n#merator dependingon the n#m!er o roots in the denominator,(e'g' (*1)6 then 89(*1)6, (7**1)7 then (8

* B)9 (7

**1)7

)- :.#ate the two sides then m#ltipl$ !$ the original%sdenominator (ever$thing sho#ld cancel and leave thevaria!les m#ltiplied the rest)- ;o solve or a varia!le, isolate the term to the originaland pl#g in the &ero o the term%s respective &erodenominator

/ARIATIONS

Direct /ariation directl$ proportional to $/,

 x=ky

Inverse /ariation is inversel$ proportional to

$/,  x=k 

 y

  0oint /ariation is directl$ proportional to $and inversel$ proportional to the s.#are o &/

 x=k   y

 x2

PRO1R2SSIONS

Arithmetic Pro-ression