4.2 adding and subtracting polynomials objective: to add and subtract polynomials. warm – up:...
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4.2 Adding and Subtracting Polynomials
• Objective: To add and subtract polynomials.
• Warm – up: Simplify:1) 6x + 7y + 4x 2) 8 + 12m – 6 + 4m
3) -(5a – 2b + 7) 4) 4z + 3 – 2 + 7z
4.2 Adding and Subtracting Polynomials
Definitionso Monomial – an expression that is
either a numeral, a variable or the product of these.
o Polynomial – a sum of monomialso Polynomials with special names:
o Binomials – a sum of two termso Trinomials – a sum of three terms
o Coefficient – the numeral within the monomial
o Similar Terms – monomials with like variables. These terms can be combined!
Exampleso 14, z, , -6x2y
o x2 + (-4x) + (-5) = x2 – 4x – 5
o 2x – 9, 2ab + b2
o x2 – 4x – 5, a2 + 3ab – 4b2
o -3xy
o -5xy2, 16yxy, xy2, -3x2y, 5xy
2
3r
4.2 Adding and Subtracting Polynomials
Name the similar polynomials:
o -2x, 2xy, 4y, x, -xy, -y
o -st2, 2s2t, 3t2s, -s2t
o 3a4, -4a3, a2, 5a3, 3a2
o x2y2, x2, y2, -3x2y2, -4x2
Simplify:o -6x3 + 3x2 + x2 + 6x3 – 5
o -3x2 + 5x – 2x + x2 – 4
o -4m2 + 5mn2 – m2 + 3mn2
4.2 Adding and Subtracting Polynomials
Find the degree.o The degree of a polynomial
is the greatest of the degrees of its terms after it has been simplified.
o 5x2yz4
o 4x3yz2
Add the Polynomialso (2x – 5) + (x + 3)
o (2a – b + 1) + (-a – b + 3)
4.2 Adding and Subtracting Polynomials
Add the Polynomials:o (2a2 + ab + 2b) +
(4a2 – 3ab + 9)
o (3x2y + 4xy2 – 2y3 + 3) + (x2y + 3y3 – 4)
o
o
6 4
4 4
a b c
a b c
3 2 2
3 2 2
3 2x x y xy
x x y xy
4.2 Adding and Subtracting Polynomials
Sum of Rectangles!o Write the sum of the
rectangles as a polynomial in simplest form. 3x 2 x x
3 3
3x 2
• Homework:– Pg. 148 Written Exercises
#1 – 20– Challenge Problems:
#31, 32, 37, 38, 41, 42