Embed Size (px)
Citation preview
1
Homework Quiz: On a separate sheet of paper, turn in the following homework problems. SHOW ALL WORK with your answer!
Bonus:
13. 17.19.
21. 25.
2
Classifying Polynomials by the Number of Terms
Number of Terms Name Example
1 Monomial x; x2; x3
2 Binomial x + 3; x2 4
3 Trinomial x2 + x + 1
4+ Polynomial x3 + x2 + x +1
Degree Type Standard Form
0 Constant f(x) = a0
1 Linear f(x) = a1x + a0
2 Quadratic f(x) = a2x2 + a1x + a0
3 Cubic f(x) = a3x3 + a2x2 + a1x + a0
4 Quartic f(x) = a4x4 + a3x3 + a2x2 + a1x + a0
Recall: Classifying Polynomials by the Degree
3
6.3 Adding, Subtracting, and Multiplying Polynomials
4
Adding or Subtracting Polynomials
To add or subtract polynomials, add or subtract the coefficients of like terms. You can use a vertical or horizontal format, whichever makes you
Ex.) (4x2 6x + 3) + (2x2 + 8x 5)
5
Ex.) (3x3 + 2x2 x 7) + (x3 10x2 + 8)
6
Ex.) (8x3 3x2 2x + 9) (2x3 + 6x2 x + 1)
7
Ex.) (3x3 + x 11) (4x3 + x2 x)
8
Multiplying Polynomials
To multiply two polynomials, each term of the first polynomial must be multiplied by each term of the second polynomial, then add the products together. Consider (x2 + 3) (x2 2x + 1)
9
10
One Method
Ex.) (x2 + 3) (x2 2x + 1)
11
Another Method
Ex.) (x2 + 3) (x2 2x + 1)
12
1.) (x 3) (2x 4)
2.) (x 2) (3x2 2x 4)
3.) (x 1) (x + 4) (x + 3)
4.) (x2 + x + 4) (2x2 x + 1)
Try the following: Find the product.
13
1.) (x 3) (2x 4)
14
2.) (x 2) (3x2 2x 4)
15
3.) (x 1) (x + 4) (x + 3)
16
4.) (x2 + x + 4) (2x2 x + 1)
17
Special Product Patterns
Sum and Difference Example(a + b) (a b) = a2 b2 (x + 3) (x 3) = x2 9
Square of a Binomial(a + b)2 = a2 + 2ab + b2 (y + 4)2 = y2 + 8y + 16(a b)2 = a2 2ab + b2 (3t 2)2 = 9t4 12t2 + 4
Cube of a Binomial(a + b)3 = a3 + 3a2b + 3ab2 + b3 (x + 1)3 = x3 + 3x2 + 3x + 1(a b)3 = a3 3a2b + 3ab2 b3 (p 2)3 = p3 6p2 + 12p 8
18
Complete the classwork sheet
Take out your student handbook and write down the homework:
pg. 341 #1361 EOO (every other odd)if necessary, Finish Classwork (will be graded)
