Warm–up #4. Warm–up #4 Solutions Homework Log Wed 9/9 Lesson 1 – 4 Learning Objective: To add,...
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Transcript of Warm–up #4. Warm–up #4 Solutions Homework Log Wed 9/9 Lesson 1 – 4 Learning Objective: To add,...
Warm–up #41. Simplify
Warm–up #4 Solutions1.=
Homework LogWed
9/9
Lesson 1 – 4
Learning Objective: To add, subtract, & multiply polynomials
Hw: #105 Pg. 36 #1 – 8 all, 9 – 61 eoo
9/9/15 Lesson 1 – 4 Polynomials
Advanced Math/Trig
Learning Objective
To add polynomials
To subtract polynomials
To multiply polynomials
To name polynomials
PolynomialsDegree of Term – sum of exponents on variables
Degree of Polynomial – largest degree among terms
Monomial – one term
Binomial – two terms
Trinomial – three terms
PolynomialsPolynomial096x – 2
– 4+ 5 + 38y
Degree Typenone monomial0 monomial1 (linear) binomial2 (quadratic)trinomial3 (cubic) binomial4 (quartic) trinomial5 (quantic) binomial
Adding & Subtracting Polynomials
1. 3 3(4 8 7) (5 3 6)x x x x Combine like terms
39 5 1x x
2. 6 2 2(6 9 5 ) (11 3 8)x x x x x Distribute (–) sign
6 2 26 9 5 11 3 8x x x x x
6 26 2 2 8x x x
cubic trinomial
degree 6 polynomial
Multiplying Polynomials
2 2(2 5 3)(4 3 )x x x x 3. 4 3 3 2 28 6 20 15 12 9x x x x x x
distribute
( 2)(4 3)x x 4. F irstO uterI nnerL ast
24 3 8 6x x x 24 11 6x x
4 3 28 14 27 9x x x x quartic poly
quadratic trinomial
Multiplying Polynomials
2
2
(5 2)(3 4)
15 20 6 8
15 14 8
n n
n n n
n n
x x
x x x
x x
5.
F irstO uterI nnerL ast
unknown degree trinomial
Box Method6. (3x – y)(x + 2y)
3
– y 3x
–xy 3
–26xy
x
2y
Vertical Method
4 2 2(3 2 )( 2 4)x x x x x 4 2
2
4 2
5 3 2
6 4 3
6 5 4 3 2
3 22 4
12 8 46 4 2
3 23 6 14 5 6 4
x x xx x
x x xx x x
x x xx x x x x x
degree 6 poly
7.
Box Method8. (x – 4)(2
2
3 2
–12–8
x
– 4
3 2 – 1
–x
4
Box Method9. ( – 3x + 1)(2
4
6 4
–9–6
2
–3x
3 2 – 1
–2
3x
2 3x –1 1
Special Product RulesDifference of two squares
(x – y)(x + y) =
Square of a binomial
Special Product RulesCube of a binomial
Special Product RulesSum of two cubes
Difference of two cubes
Multiply9. (3x – (3x +
Difference of Squares
9
Quartic Binomial
Multiply10. = (3x + 4)(3x + 4)
Square of a binomial
9
Quadratic Trinomial
Multiply11.
Square of a binomial
25
Degree 6 Trinomial
Multiply12.
Cube of a binomial
Cubic Polynomial
Multiply13. + 2xy + 4
Difference of two cubes
Cubic Binomial
Ticket Out the Door
Express without absolute values if x < 2
Explain how you came up with your answer
Homework#105 Pg. 36 1 – 8 all, 9 – 63
odd &
name answer by degree & # of terms