Math formulas we gotta memorize

The Pythagorean Theorem

The Pythagorean Theorem

Given any right triangle, a²+b²=c²

Quadratic Formula

x = -b +- (sq root of b-4ac)/(2a)

Difference of Squares

a²-b²= (a+b)(a-b)

Difference of Cubes

a³-b³= (a-b)(a²+ab+b²)

Sum of Cubes

a³-b³= (a-b)(a²-ab+b²)

Perfect Square Trinomial

a²-ab+b²= (a-b)²

a²+ab+b²= (a+b)²

Trinomial of the Form

x² +bx +c = (x+m)(x+n)

The Remainder Theorem

If polynomial, P(x)/(x-c), remainder = P( c )

The Factor Theorem

c is root fo P(x), if and only if (x-c) is a factor of P(x)

The fundamental theorem of Algebra

nth degree polynomial function w/ complex coefficent & n>=1, and at least a complex zero.

P(x) = a(x-c1)(x-c2)….(x-cn)

Rational zeroes theorem

Given a nth degree polynomial function,

P(x)=anx^n+an-1x^n-1+…+a2x²+a1x+a0

an doesnt = 0 a0 doesnt = 0

P(x) is a form of p/q (p being a factor of a0 & q being a factor of an)

Descartes’ Rule of Signs

Given a polynomial function w/ real coefficents

P(x)=anx^n+an-1x^n-1+…+a2x²+a1x+a0

m= # of sign changes in the coefficients of P(x), # of pos, real zeroes of P(x) = m or < m by an even #.

n= # of sign changes in the coefficients of P(-x), # of neg, real zeroes of P(x) = n or < n by an even #.

Arithmetic Seq

a1 is the intial form, d is the common difference

a1, a2 = a1 +d, a3= a1+2d, a4= a1+3d…

Formula (nth term): an = a1 +(n-1)d

Formula (Sum) Sn= n(a1-rn)

Geometric Sequences

Infinite Geometric Series

The Binomial Theorem

Basic Trigonometric Identities

Even/Odd Properties

sin(-x)=-sin so the sine function is an odd function.

cos(-x)=, cos x so the cosine function is an even function.

Sum and Difference Formulas

Double Angle Formulas