Math Mini Project 2 Sequences, Series, and Solving

Convert it into (x ± ?)(x ± ?) where the two ? add up to b and multiply to c. Afterwards, you multiply the two together to get another quadratic equation.

Similar to factoring x² + bx + c but instead to form is converted into (ax ± ?)(ax ± ?) where the two a’s must have a product that equals a in the equation. Afterwards multiply the two together to get another quadratic equation.

Very simple, simply converts to (a + b)(a - b) using the difference of two squares or DOTS

Use the cube formula: a³ - b³ = (a - b)(a² + ab + b²)

or a³ + b³ = (a + b)(a² - ab + b²)

Factor out the greatest common factor in an equation, then split the equation within the parentheses into two different terms, then rewrite the pairs of terms and take out the common factor.

Factor the quadratic equation the same way you would factor ax² ± bx ± c. (fx ± d)(gx ± e) where the two solutions would be x = ± d/f and x = ± e/g

Quadratic Formula: x = (-b ± √(b² - 4ac)) / (2a)

Note: use plysmlt on Calculator for quadratic equation.

Use the Change of Base Formula: logₐ(b) = log(c) / log(a)

Dropping the base of a logarithmic equation is when both logarithms in the equation have the same base so you just remove the logarithim and solve

Rewrite the equation as an exponential equation

logₐ(x) = b => x = a^b

When solving exponential equations with the same base, set the exponents equal to each other and solve for the variable.

Keep the exponential expression on one side of the equation, get the logarithms of both sides of the equation using any base, solve for the variable.

When solving a quadratic equation, you can substitute certain terms with U which will simplify the equation where you can solve it. Afterwards, you will plug in what you got for U into what U represents in order to find the actual equation.

After you have graphed your equation, press 2nd →trace →Value →plug in the x value

APP contains polysmlt which allows you to solve for the solutions in quadratic equations

un = u1 + (n-1)d

Sn = (n/2)(2u1 + (n-1)d)

un = u1r^n-1

Sn = u1(r^n - 1)/(r - 1)

Sinfinity = u1/(1 - r)

I = Prt

I = interest

P = original amount

r = interest rate

t = time

I = P x (1 + r/(100k)^kn

I = interest

P = final value

r = interest rate

k = compounding periods per year

n = number of years

(a + b)^n = a^n + ^nC1(a^(n-1)b) + … + ^nCr(a^(n-r)b^r) + …. + b