Unit 4 - Polynomials

a a a a -p2 -p2 Reminder – the coefficient means “how many of them there are”.

c c m2 m2 m m m

h2 h2 h h h h h h

m m m m m x2 x2 x2 r r r r r r2 r2 x x x x x m2 m2 r2 m2

-w2 -w2 x2 x2 -w2 w w w w x x x x x

b2 b2 -x2 -x2 Monomial because there is only one kind of term a a a a Binomial – 2 different terms Trinomial – three different terms

2x2 – 8x + 2 – 4x + 6 2x2 – 8x + 2

-2q2 +5q - 2 q - 8 2q2 – 8q + 3

Class Work P. 214 #4-7, 9-17

Algebra Tile Exercise Find a partner and a bag of algebra tiles. Without looking, take out some algebra tiles and place them flat on your desk. Each partner will write down an expression to represent the tiles. Check your answer with your partner. Each partner will then simplify your expression by collecting like terms. Check. 12 minutes.

Collecting Like Terms

Terms Variables – letters that represent unknown numbers. (a,b,x) Coefficients – are numbers in front of the variables. (4a, 2b, 200x) Terms – are made up of variables and coefficients. (4a, 2b, 200x)

Like Terms Terms with identical variables and exponents are like terms. EXAMPLE: y, 3y, -2y are like terms 2x, 2g, 2k are not like terms Basically the variable and exponent has to be the same.

Like Terms Also the variable needs to be to the same exponent to be like terms. Example: y2, -2y2, 45y2 are like terms y, -20y2, 5y3 are not like terms The exponent has to be the same number.

Try These Which are like terms? Why? 5b, 3g, -2g, 2g2, 5g, ½g, -g

Solution: Which are like terms? Why? 5b, 3g, -2g, 2g2, 5g, ½g, -g Yellow – like terms. ( they all have the same variable and the same exponent) White – not like terms.

Combining Like Terms x + x + x + x + x There are five variables which are like terms therefore we simply add them like we would if they were numbers. x + x + x + x + x = 5x

Combining Like Terms Example 1 4t + 3t + t = 8t

Combining Like Terms Rearrange the variables so that all like terms are side by side. Example 2 2t2 + 8 – 5t2 = 2t2 – 5t2 + 8 (notice that the –negative stayed with –5t2 ) = -3t2 + 8

Combining Like Terms Example 3 2t + 3t2 – 2t –t2 = 3t2 – t2 + 2t – 2t (collecting like terms) = 2t2 + 0 = 2t2

Combining like terms 3ab + 4a – 3b + 4ab – 7a + 2b = 3ab + 4ab + 4a – 7a – 3b + 2b = 7ab -3a – b Finished the question because none of the variables are the same.

Class Work P. 222 #4-15

Class work Worksheet