Operations with Polynomials
Solve by Factoring
Writing Equations and Sketching Graphs
Degree and y-int
Misc. Choose at your Own Risk!
100
Add the Polynomials
(4x + 9) +(x - 4)
5x + 5
100
Solve by factoring:
x2 - 25=0
x=-5 and x=5
100
Write a polynomial function that has zeros x = 8, x = -1 and x = 3.
y = (x - 8)(x + 1)(x - 3)
100
What is the degree and y-int of y = 4x2 - 5x + 3
degree: 2
y-int: 3
100
Ryan is making a box out of cardboard the size of 15 by 7 inches. Write the formula for the volume of the box.
V = x(15 - 2x)(7 -2x)
200
Add the polynomials:
(-5x2+3x6+5) + (-5x6-5-3x2)
-2x6-8x2
200
Solve by factoring:
3x2 - 3x - 60=0
x=-4 and x=5
200
Write x = -3, x = 1/2, x = 8 as a polynomial WITHOUT a fraction
y = (x + 3)(2x - 1)(x - 8)
200
What is the degree and y-int of y = 3x2 - 8x3 + 7
degree: 3
y-int: 7
200
Given the formula for the volume of this specific box (not correlated to any other problem here), what is a reasonable domain?
V = x(10 - 2x)(8.5 -2x)
0 < x < 4.25
300
Multiply the Polynomials:
(2x-6)2
4x2 -24x +36
300
Solve by factoring:
x2 + x - 6 = 0
x=2 and x=-3
300
Given f(x) = x3 -2x2 + cx - 10, for what value of c is (x - 2) a factor of f(x)?
c = 5
300
What is the degree and y-int of y = (x - 5)(x + 3)(x - 4)
degree: 3
y-int: 60
300
For the polynomial function f(x)=x3-2x2-5x+6, we have f(0)=6, f(-2)=0, f(3)=0, f(1)=0. Rewrite f(x) as a product of linear factors
f(x)=(x+2)(x-3)(x-1)
400
Multiply the Polynomials:
(4n - 1)(3n + 4)
12n2 + 13n - 4
400
Write x3-x2-22x+40 as a product of linear factors given x-2 is a factor
(x-2)(x-4)(x+5)
400
Given y = (x - 4)(x + 5)(x - 1), sketch the graph and write the end behavior
EB: down, up
400
What is the degree and y-int of y = 5(x - 3)(x + 4)(x - 1)
degree: 3
y-int: 60
400
Find the intersection of (x - 4) = (x - 4)(x + 3)
x = 4, y = 0
x = -2, y = -6
500
Multiply the Polynomials:
(d + 3)(d2 - 4d + 1)
d3 - d2 -11d + 3
500
Write x3-73x-72 as a product of linear factors given x+1 is a factor
(x+8)(x+1)(x-9)
500
Given y = (x - 2)2(x + 1)3(x + 2), sketch the graph and write the end behavior
EB: up, up
500
What is the degree and y-int of y = (x - 4)2(x + 1)3(x - 2)
degree: 6
y-int: -32
500
Find the intersection of f(x) = 2(x+5) and g(x) = (x + 5)(x - 8)
x = 10, y = 30
x = -5, y = 0