Lesson 53 Adding and subtracting polynomials monomial A

Lesson 53 Adding and subtracting polynomials

monomial A monomial is the prodeuct of numbers and/or variables with whole number exponents. The degree of the monomial is the sum of the exponents of the variables in the monomial. A constant has a degree of 0.

Finding the degree of the monomial -7 x 2 yz 3 add exponents degree is 2+1+3 = 6 8 xy 2 z " 1+2+1 = 4 122 ab 3 c " 1+3+1= 5 (3. 54)abc 5 7 xy 3 z 2 102 ab 3 c

polynomial A polynomial is a or the sum or difference of monomials. A polynomial with 1 term is a monomial Example: 6 x A polynomial with 2 terms is a binomial Example: 6 x + 10 A polynomial with 3 terms is a trinomial Example: x 2 + 6 x - 10

Degree of a polynomial The degree of a polynomial is the degree of the greatest degree term in the polynomial Example: 5 x 3 y 2 z-3 x 4 y 3 + 6 xyz Degrees 6 7 3 so this is a 7 th degree polynomial

Leading coefficient The leading coefficient for a polynomial is the coefficient of the term with the highest degree. Example: 2 x 4 + 5 x 5 - 6 x 2 Degrees 4 5 2 so leading coefficient is 5

Standard form of a polynomial The standard form of a polynomial is a form of a polynomial where terms are ordered from greatest to least degree. Example: 8 xy 2 - 9 + 5 x 3 y 3 z degrees 3 0 7 standard form: 5 x 3 y 3 z + 8 xy 2 - 9

Writing in standard form Write in standard form and find the leading coefficient: 2 n 2 + n 3 9 x 2 y - 3 x 2 y 2 - 5 xy 8 + 5 x 2 - x + 7 x 3 3 a 2 b - 2 b 4 + 5 - 6 ab 3 xy - 2 x 2 y - 7 x 3 y 2

Adding & subtracting polynomials To add or subtract polynomials, combine like terms (-8 x 3 + 4 x 2 + x + 1) + (3 x 3 - 2 x 2 + 7) Remove parentheses and add like terms -5 x 3 + 2 x 2 + x + 8 Try: (-2 a 4 + 3 a 2 - 6 a + 5) + ( a 2 + a -8)

Subtracting polynomials When subtracting, be sure to distribute the negative. (6 x 2 + 4 x + 2) -( 2 x 2 -x + 8) 6 x 2 + 4 x + 2 -2 x 2 + x - 8 Combine like terms 4 x 2 + 5 x -6

practice (4 z 2 - 5 z + 3) - ( 2 z 2 + 7 z + 3) (m 2 - 7 m 3 - m -3) -( 10 m 3 + m + 2 - m 2) (x 2 + 4 x -9) - ( 4 x 2 - 5 x + 11) (2 a+3 b) - (5 b-2 c) + (3 a-7 c) (8 a + 5 b) - (3 b - 2 a) - (3 a + 5 b)