What do these prefixes mean Can you give

What do these prefixes mean? Can you give a word that starts with them? MONO BI TRI POLY

Term A number, a variable, or the product/quotient of numbers/variables. Examples?

Degree of a Term The exponent of the variable. We will find them only for one-variable terms.

Term Degree of Term 3 0 4 x 1 -5 x 2 2 18 x 5 5

Polynomial A term or the sum/difference of terms which contain only 1 variable. The variable cannot be in the denominator of a term.

Degree of a Polynomial The degree of the term with the highest degree.

Polynomial Degree of Polynomial 6 x 2 - 3 x + 2 2 15 - 4 x + 5 x 4 4 x + 10 + x 1 x 3 + x 2 + x + 1 3

Standard Form of a Polynomial A polynomial written so that the degree of the terms decreases from left to right and no terms have the same degree.

Not Standard 6 x + 3 x 2 - 2 3 x 2 + 6 x - 2 15 - 4 x + 5 x 4 - 4 x + 15 x + 10 + x 2 x + 10 1 + x 2 + x 3 x 3 + x 2 + x + 1

Naming Polynomials are named or classified by their degree and the number of terms they have.

Polynomial Degree Name 7 0 constant 5 x + 2 1 linear 4 x 2 + 3 x - 4 2 quadratic 6 x 3 - 18 3 cubic For degrees higher than 3 say: “nth degree” x 5 + 3 x 2 + 3 x 8 + 4 “ 5 th degree” “ 8 th degree”

Polynomial # Terms Name 7 1 monomial 5 x + 2 2 binomial 4 x 2 + 3 x - 4 3 trinomial 6 x 3 - 18 2 binomial For more than 3 terms say: “a polynomial with n terms” or “an n-term polynomial” 11 x 8 + x 5 + x 4 - 3 x 3 + 5 x 2 - 3 “a polynomial with 6 terms” – or – “a 6 -term polynomial”

Polynomial Name -14 x 3 cubic monomial -1. 2 x 2 quadratic monomial -1 constant monomial 7 x - 2 linear binomial 3 x 3+ 2 x - 8 cubic trinomial 2 x 2 - 4 x + 8 quadratic trinomial x 4 + 3 4 th degree binomial

9. 1 Adding and Subtracting Polynomials Adding Polynomials in horizontal form: (x 2 + 2 x + 5) + (3 x 2 + x + 12) = 4 x 2 3 x + 17 + in vertical form: x 2 + + 2 x + 5 3 x 2 + x + 12 2 = 4 x + 3 x + 17

9. 1 Adding and Subtracting Polynomials Simplify: The classify the polynomial by number of terms and degree x 2 +x + 1+ 2 x 2 + 3 x +3 x 22 + 4 x + 3 (4 b 2 + 1) + 3 x 2 – 4 x + + 82 x 2 – 7 x – 5 x 52 – 11 x + 3 2 b + (7 b 2 + b 2– 3) 11 b + 3 b – 2 – 5 a 2 + + 3 a 2 + 2 a – 7 2 4 a + 10 a – 12 8 a

9. 1 Adding and Subtracting Polynomials Simplify: The classify the polynomial by number of terms and degree 7 d 2 + 7 d + 2 d 2 + 3 d 9 d 2 + 10 d (2 x 2 5) – 3 x + + (4 x 2 + 7 x – 2) 6 x 2 + 4 x + 3 z 2 + 5 z ++4 2 z 2 -5 3 z 2 + 5 z – 1 (a 2 – 4) + + (8 a 29 a – 28 a)– 2 a – 4 6 a

9. 1 Adding and Subtracting Polynomials Simplify: The classify the polynomial by number of terms and degree 3 d 2 + 5 d 1 2 – + –(– 4 d 5 d + 2) –d 2 + 1 (3 x 2 + 5 x) + (4 – 6 x – 2 x 2) x 2 4 –x+ + 3) 7 p 2 5 2 – 2 p + + (– 5 p (x 3 + 7) 2 p 2 – 2 p + 8 + x 2 + (2 xx 23 + + 3 x 3 x 2–+8)3 x – 1

9. 1 Adding and Subtracting Polynomials Simplify: 2 x 3 + x 2 + – 43 x 2 – 9 x + 7 2 x 3 + 4 x 2 – 9 x +3 8 5 y 2 4 p 2 + 5 p+ (-2 p + 7) 2 4 p + 7 – 3 y + 3 – 9 + 4 y 4 y 3 + 5 y 2 – 3 y – 1 4 c) (8 cd – 3 d + +4 c(-6 ++ 2 cd – 4 d) – 7 d 10 cd – 6

9. 1 Adding and Subtracting Polynomials Simplify: (12 y 3 + y 2 – 8 y + 3) + (6 y 3 – 13 y + 5) = 18 y 3 y 2 – 21 y + 8 + (7 y 3 + 2 y 2 – 5 y + 9) + (y 3 – y 2 + y – 6) = 8 y 3 + y 2 – 4 y + 3 (6 x 5 + 3 x 3 – 7 x – 8) + (4 x 4 – 2 x 2 + 9) = 6 x 5 2 x 2 – 7 x + 1 + 4 x 4 + 3 x 3 –

Subtracting Polynomials ubtraction is adding the opposite) (5 x 2 + 10 x + 2) – (x 2 – 3 x + 12) – 12) (5 x 2 + 10 x + 2) + (–x 2) + (3 x) + ( = 4 x 2 + 13 x – 10 5 x 2 + 10 x = 5 x 2 + –(x + 22– 3 x + 12) = –x 10 x +2 2+ 3 x – 12 4 x 2 + 13 x – 10

9. 1 Adding and Subtracting Polynomials Simplify: (3 x 2 – 2 x + 8) – (x 2 – 4) 3 x 2 – 2 x + 8 + (– x 2) + 4 = 2 x 2 2 x + 12 – (10 z 2 + 6 z + 5) – (z 2 – 8 z + 7) 7) 10 z 2 + 6 z + 5 + (–z 2) + 8 z + (– = 9 z 2 14 z – 2 +

9. 1 Adding and Subtracting Polynomials Simplify: –– (5 a 2 a 2 – 5 a 7 a 2 + 3 a) 2 a 2 4 x 2 + 3 x + 2 2 – 3 x – (2 x – 7) 2 x 2 + 6 x +9 3 x 2 – 7 x – +(x 52 + 4 x + 7) 2 x 2 11 x – 2 – 7 x 2 – x + 3 – (3 x 2 – x – 7) + 10 4 x 2

9. 1 Adding and Subtracting Polynomials Simplify: 3 x 2 2 –+ (2 x 10 6) x 2 – 2 x + 4 x – 2 x 2 2 – 3) – + (x 5 x – 6 x x 2 + 16 +3 3 x 2 3 2–x – (2 x x 2 +7 – 5 x + – 4) – 4 x + 5 x 4 x 2 – x + 6 – (3 x 2 – 4) + 10 x 2 –x

9. 1 Adding and Subtracting Polynomials Simplify: + 5) (4 x 5 + 3 x 3 – 3 x – 5) – (– 2 x 3 + 3 x 2 + x = 4 x 5 4 x – 10 – 9) + 5 x 3 – 3 x 2 – (4 d 4 – 2 d 2 + 2 d + 8) – (5 d 3 + 7 d 2 – 3 d = 4 d 4 5 d + 17 (a 2 – 5 d 3 – 9 d 2 + + ab – 3 b 2) – (b 2 + 4 a 2 – ab) = – 3 a 2 – 4 b 2 + 2 ab

9. 1 Adding and Subtracting Polynomials Simplify by finding the perimeter: 6 c + 3 A c 2 + 1 4 c 2 + 2 c + 5 A= 5 c 2 x 2 + x + 8 c + 9 2 x 2 B x 2 + x B = 6 x 2 + 2 x 2 x 2

9. 1 Adding and Subtracting Polynomials Simplify by finding the perimeter: 3 x 2 – 5 x x 2 +7 C 2 d 2 + d – 4 3 d 2 – 5 d D 3 d 2 – 5 d d 2 + 7 C = 8 x 2 – 10 x + 14 D = 9 d 2 – 9 d + 3

9. 1 Adding and Subtracting Polynomials Simplify by finding the perimeter: 3 x 2 – 5 x a+1 E a 3 + 2 a 2 a 3 + a + 3 E = 3 a 3 + 4 a + 4 x 2 + 3 F F = 8 x 2 – 10 x + 6

HW: Section 9. 1 Page 459 (2 -26 even)