Adding and Subtracting Polynomials
(-4x^2-6x+18)+(-x^2+7x+8)
-5x^2+x+26
(x-5)(x+3)
x^2-2x-15
(2x^4+3x^3+5x-1)/(x^2+3x+2)
2x^-3x+5+(-4x-11)/(x^2+3x+2)
(-x^3+4x^2+9)/(x-3)
-x^2+x+3+(18/(x-3))
What are like terms?
Terms with same variables and exponents
(48+6x^2-12x)-(-x^2+24x-63)
7x^2-36x+111
(4x-3)(2x+7)
8x^2+22x-21
(X^3-x^2-2x+8)/(x-1)
x^2-2+(6/(x-1))
(x^3-x^2-9x+18)/(x+3)
x^2-5x+6
What is a binomial?
An expression with 2 terms.
(x^3+x^2-3x+5)-(-x^3+6-5x^2)
2x^3+6x^2-3x-1
(3x-5)(3x+5)
9x^2-25
(x^4+2x^2-x+5)/(x^2-x+1)
x^2+x+2+(3/(x^2-x+1))
(3x^3-2x^2+2x-5)/(x+1)
3x^2-5x+7-(12/(x+1))
What is a linear factor?
A factor with the highest degree of 1 written in the form (x-k)
(-11x^4-x^3-3x^2+10x-2)-(-11x^4+5x^2-7x+13)
-x^3-8x^2+17x-15
(3x+1)(x^2+8x+7)
3x^3+25x^2+29x+7
(x^2+x-17)/(x-4)
x+5+(3/(x-4))
Evaluate the function using Synthetic Division
f(x) = 5x^3-x^2+13x+29
when x=-4
f(-4)=-359
What is Pascal's Triangle?
A shortcut method to multiply polynomials with binomial expansion.
(xy^2+a-b-x^2y)-(5xy^2-3a+b+3x^2y)
-4xy^2-4x^2y+4a-2b
(2x-5)^4
16x^4-160x^3+600x^2-1000x+625
(3x^2-14x-5)/(x-5)
3x+1
Evaluate the function using synthetic division
f(x) = 5x^4+2x^3-20x-6
when x=2
f(2)=50
What is the perfect cube pattern?
a^3+3a^2b+3ab^2+b^3