Evaluate and Classify
Is this a polynomial? Explain why or why not.
f(x) = x2-2x-x-3+2
No, x is not a whole number and -3 is not a whole number (the exponents)
Find the Product: (x2+4)(2x+8)
2x3+8x2+8x+32
What are the different methods we use to factor cubics?
Factor by grouping, GCF, sum/difference of cubes
What is the Rational Root Theorem / what do we use it for?
Used to find all the possible solutions of a polynomial - then we find the actual roots
What conditions must be met to use synthetic division?
divisor must be a linear binomial
Evaluate: x4-7x3+x-1 when x=1
-6
Find the Sum: (2x+5) + (4x+1)
6x+6
Factor completely: 8x2-125x
x(8x-125)
Describe the transformations: g(x)= -(x+1)3+4
reflect over the x-axis, left 1, up 4
What two things do we use synthetic division for?
dividing polynomials and finding roots
f(x)=-3x+4-x3+x2
Name the type of polynomial, the degree, the leading coefficient, number of terms, and constant.
Type: cubic
Degree: 3
Leading Co: -1
Terms: 4
Constant: 4
Simplify: (-13x2-8x4-3x) - (5x2+3x-2)
-8x4-18x2-6x+2
(x+6)(x2-2)
Write a rule for the transformation: translation 5 units up, followed by a reflection in the y-axis.
f(x) = -2x3-12
g(x) = 2x3-7
What are turning points, and what are the specific names we can give the two that fall on a cubic graph?
where the graph changes from increase to decrease and vice versa
local maximum and local minimum
Describe the end behavior of this cubic polynomial - based on the leading coefficient: x3+5x2-71x+15
as x goes to positive, y also goes to positive
as x goes to negative, y also goes to negative
Find the Quotient: (x3+10x2+23x+17) / (x+2)
x2+8x+7+3/x+2
Factor completely: 8x3-1
(2x-1)(4x2+2x+1)
Find all the real solutions using rational root theorem: 3x3-2x2-12x+8
x= -2, 2, 2/3
What do the Factor Theorem and Remainder Theorem tell us?
If we have a remainder of 0, the divisor is a factor. If the remainder is not zero, then the divisor is not a factor.
Evaluate: -2x3+7x2+5x-1, when x = 3
101
Find the area of the shaded region (on the board)
*hint: area of triangle = 1/2(base)(height)
15/2 x +15
Factor completely: 18x3-2x
2x(3x-1)(3x+1)
Write a cubic function using the points from its graph: (-4,0), (0,6), (2,0), and (4,0)
y=3/16 (x+4)(x-2)(x-4)
Write a polynomial function to model the data from the table (see board)
f(x) = 2x3-7x2-6x