World 2-1 Adding and Subtracting Polynomials

Recall;

A monomial is a single algebraic term.

A binomial contains two unlike terms

A trinomial has 3 unlike terms

Two terms are like terms, if they have the same variables, raised to the same exponents. Order is not important.

eg. 1YES

YES

NO

The DEGREE of a monomial is the sum of all its powers.

eg. 2

2 6 Not Not 11

To be a monomial, the exponent must be a positive whole number. No fractions and no negatives.

Polynomials can be simplified by combining like terms.

When adding like monomials, simply add the coefficients and keep the exponents the same.

eg. 3

eg. 4 Combine the following like terms

eg. 5 Simplify

Simply remove bracketswhen adding

(a)(4y2 – 4) – (10y2 – 2x4 + 6)

c) (6m2 + 17m – 4) – (2m2 – 13m – 3)

b) (3a2 + 2a - 2) - (a2 - 3a + 7)

= 4y2 – 4 – 10y2 + 2x4 – 6= 2x4 + 4y2 – 10y2 – 4 – 6= 2x4 – 6y2 – 10

= 3a2 + 2a – 2 - a2 + 3a + 7= 3a2 - a2 + 2a + 3a + 7= 2a2 + 5a + 7

= 6m2 + 17m – 4 – 2m2 + 13m + 3= 6m2 – 2m2 + 17m + 13m – 4 + 3= 4m2 + 30m -1

eg. 6 Change the sign of everything in the bracketsbeing subtracted

Homework

World 2-2