Polynomial Operations
When subtracting polynomials, we must first "______" the negative sign to all the terms before combining "____" terms.
"distribute" and "like"
When multiplying variables, we "___" the exponents.
add
#16 on Review
Identify the Degree and Sign of the leading term.
f(x) = x3(x-4)2(x+2)3
Degree: 8 (even); Leading term: 1 (positive)
#10 on Review
Find each coefficient described.
Coefficient of 4th term of (2y+1)5
40
The Binomial Theorem hinges on "________" triangle.
Pascal's
#1 on the review
(9n4-3-2n2) + (14n4-3n5+13n2)
-3n5+24n4+11n2-3
We are going to use the "________ __________" when multiplying polynomials.
distributive property
#18 on Review
Identify each zero and their multiplicity. (And what they do on the graph: cross, bounce, or flex)
f(x) = x3(x-4)2(x+2)3
cross at (0,0), bounce at (4,0), and cross at (-2,0)
#11 on Review
Find each coefficient described.
Coefficient of 2nd term of (1+2n)5
10
#13 on Review
Find the term described.
4th term in expansion of (2a+1)6
160a3
#2 on Review
(-4x4+7x-2x5) - (4x4+9x-12x2)
-2x5-8x4+12x2-2x
What is the method used to divide polynomials called?
Polynomial Long Division
#20 on Review.
Identify the end behavior.
f(x) = x3(x-4)2(x+2)3
As x -> infinity, y -> infinity
As x -> negative infinity, y -> infinity
#12 on Review
Find each coefficient described.
Coefficient of 3rd term of (3n+1)5
270
#14 on Review
Find the term described.
3rd term in expansion of (2x+1)6
240x4
#3 on Review
(-5k+5)(-2k-6)
10k2+20k-30
#5 from Review
Divide. (m4-m3-40m2+6m-28) / (m+6)
m3-7m2+2m-6 r.8
#17 on Review
Identify the Degree and Sign of the leading term.
f(x) = -4x2(x-1)6(x+8)7
Degree: 15 (odd); Leading Term: -4 (negative)
Set up the expansion.
(2a-b)4
1(2a)4(-b)0 + 4(2a)3(-b)1 + 6(2a)2(-b)2
+ 4(2a)1(-b)3 + 1(2a)0(-b)4
#15 on Review
Find the term described.
3rd term in expansion of (1+2x)6
60x2
#4 on Review
(7x2-4x+6)(-2x2-5x+7)
-14x4-27x3+57x2-58x+42
#6 from Review
Divide. (5n4+11n3+2n2-5n-1) / (n+1)
5n3+6n2-4n-1
#19 on Review.
Identify each zero and their multiplicity. (And what they do on the graph: bounce, cross, or flex)
f(x) = -4x2(x-1)6(x+8)7
bounce at (0,0), bounce at (1,0), and cross at (-8,0)
Set up the expansion for
(x-3y)4
1(x)4(-3y)0 + 4(x)3(-3y)1 + 6(x)2(-3y)2
+ 4(x)1(-3y)3 + 1(x)0(-3y)4
Set up the expansion for (2x+y)6
1(2x)6(y)0 + 6(2x)5(y)1 + 15(x)4(y)2 + 20(2x)3(y)3 + 15(2x)2(y)2 + 6(2x)1(y)5 + 1(2x)0(y)6