cubes
September 09, 2016
Objective: Polynomial Long Division and Long Division of Cubes
Warmup: Divide: Then continue Ex. 3 and 4 from yesterday's notes: Ex 3: 4. cubes
September 09, 2016
Objective: Polynomial Long Division and Long Division of Cubes
Warmup: Divide:
cubes
September 09, 2016
Ex 3: 4. cubes
September 09, 2016
HW #1 Solutions:
1
cubes
September 09, 2016
In pairs, divide each of the following using polynomial long division.
Ex 1)
Ex 4)
Ex 2)
Ex 5)
Ex 3)
Ex 6)
cubes
September 09, 2016
cubes
September 09, 2016
Look over all of your answers. Did you notice a pattern???
Try these using the pattern to solve without dividing:
7)
9)
8)
10)
cubes
September 09, 2016
We can use a similar technique to factor the sum and difference of Ex 1)
3 ± b3.
cubes in the form a
Take the cube root of each term to get the divisor (the binomial) and use the pattern to get the trinomial.
a3 + b3 = (a + b)(a2 ­ ab + b2)
a3 ­ b3 = (a ­ b)(a2 + ab + b2)
same
sign
different
signs
always
a+
cubes
September 09, 2016
Factor using the patterns we discovered:
Ex 1)
11. 12. 13. 14.
cubes
September 09, 2016
cubes
September 09, 2016
Long Division is just another form of factoring!! Sometimes you can factor and simplify the fraction instead of using division.
Divide the following polynomials by factoring and numerator and simplifying. Ex 1)
2)
cubes
Ex 1)
3. 4.
September 09, 2016
cubes
September 09, 2016
Ex 1)
5.
6.
7.
cubes
September 09, 2016
Practice: Divide each of the following:
1.
4.
2.
5.
3.
6.
cubes
September 09, 2016
HW #2: Pg. 65 #'s 57 ­ 64 all
cubes
September 09, 2016
cubes
September 09, 2016
Factor
Ex
1) each of the following.
Ex 10) x3 - 64
Ex 11) y6 + 216z3
Ex 12) 125x3 - 8
cubes
September 09, 2016
Practice: Factor.
1) x3 + 1000
2) 8a3 - b12
3) 1 + 27x6