Monomials, Binomials, and Polynomials
the terms 4a²b² , -9a²b²
like terms
Change the signs of ALL of the terms being subtracted. Change the subtraction sign to addition. Follow the rules for adding signed numbers. Ex. (2x² - 4) - (x² + 3x - 3)
horizontal method
Combining like terms
adding and subtracting polynomials
the sum of two monomials
binomial
they can be combined by addition or subtraction
coefficients
Arrange the like terms so that they are lined up under one another in vertical columns. Now, change signs of all terms being subtracted and follow rules for add. Ex. 2x² + 0x - 4 - (x²+ 3x - 3)
vertical method
Like terms are ....
terms that have the same variables and same exponents on those variables.
the product of non-negative integer powers of variables
monomial
the terms x² , x , 2ab
unlike terms
(-2x² - 14) + (7x² + 3x + 3)
5x² + 3x - 11
(2x² - 4) - (x² + 3x - 3) -----> x² - 3x - 1
2x² - 4 - x² - 3x + 3
The method of grouping like terms and solving.
horizontal method
x² + 2x + 1 + 3x² - 4x becomes 4x² - 2x + 1
simplest form of polynomials
-14xy , 14 xy , xy
like terms
x² - 6x + 4 + x² + 3x - 3 -----------------
2x² - 3x + 1
2x² + 0x - 4 - (x²+ 3x - 3) ---------------- x² - 3x - 1
2x² + 0 - 4 - x² - 3 x + 3
Prefix meaning "many".
poly
4x² - 2x + 1 exponents of variables decrease from left to right
descending order
monomials that have the same variable factors
like terms
(5x² – 1) + (10x³ + 21x² - 7x)
(10x³ + 26x² - 7x - 1)
3x² and 2x² of the polynomial (3x² - 1) - (2x² + 7x)
like terms
Prefix that means "one".
mono