Properties of Polynomials
Write in Standard Form, Then find the Degree and number of terms:
1 - 2s + 5s^4
What is:
5s^4 − 2s + 1;
quartic trinomial
Find The Zeroes of:
y = (x + 2)(x - 3)
What is -2 and 3?
The side of a cube measures 3x + 2 units long. Express the volume of the cube
as a polynomial.
What is: 8x^3 + 12x^2 + 6x + 1?
Divide (x2 + 8) by x-4. Give the Quotient and Remainder.
What is Quotient: x+4 Remainder 24?
Find the real or imaginary solutions of the equation by factoring.
x3 + 512 = 0
Hint: write x3 + 512 as a sum of cubes and factor
( x3 + 83 = 0)
.
What are x = -8, 4 + 4i*sqrt(3), 4 - 4i*sqrt(3)?
Write in Standard Form, Then find the Degree and number of terms:
x(x + 5) - 5(x + 5)
What is:
x^2 − 25; quadratic
binomial
Write in Factored Form:
2x^3 + 10x^2 + 12x
What is: 2x(x+2)(x+3)?
The product of three consecutive integers is 720. What are the numbers?
What is: 8, 9 and 10?
Divide (x3 - 15) by x-1. Give the Quotient and Remainder.
What is Quotient: x2+x+1 Remainder: -14?
Find the real or imaginary solutions of the equation by factoring.
x4 - 3x2 = -2x2
What are x = 0, 1, −1?
Determine the degree of the polynomial given:
x: -2 -1 0 1 2
y: -16 1 4 5 16
What is: Degree 3?
Find Maxima and Minima of:
f(x) = x^3 - 7x^2 + 10x
What is:
Max at: 4.06
Min at: -8.21
The height of a box is 3 cm less than the width. The length is 2 cm less than the width. The volume is 50 cm^3. What is the width of the box?
What is 5.54 cm?
Divide (3x3 - 70x + 2) by x-5. Give Quotient and Remainder.
What is 3x2+15x+5 Remainder 27
Find the real or imaginary solutions of the equation by factoring.
x3 + 5x2 = 6
What are x= {-1, 1, i*sqrt(6), -i*sqrt(6)}?
Determine the End Behavior of the following Polynomial:
Y=12x^4 - x + 3x^7 - 1
What is Down and Up?
Write in Factored Form:
x^3 - 2x^2 + x
What is: x(x − 1)^2?
Your sister is 8 years older than you. Your mother is 25 years older than your sister. The product of all three ages is 18,816. How old is your mother?
What is 49 Years old?
Use synthetic division and the given factor to completely factor the polynomial function.
y = 2x3 + 9x2 + 13x + 6; (x + 1)
What is: y = (x + 1)(x + 2)(2x + 3)?
Solve.
2x3 + 8x2 + 4x = -16
What is: x= {-4, i*sqrt(2), -1*sqrt(2)}
Write in Standard Form, Then find the Degree and number of terms:
(2x^4 + 4x - 5)/4
What is: 0.5x^4 + x −5/4; quartic trinomial
Write in Factored Form:
x^3 + 7x^2 + 15x + 9
What is: (x+3)^2 * (x+1)
A rectangular box is 24 in. long, 12 in. wide, and 18 in. high. If each dimension is increased by x in., what is the polynomial function in standard form that models
the volume V of the box?
What is x3 + 54x2 + 936x+5184 Inches cubed?
Use synthetic division and the given factor to completely factor the polynomial function.:
y = x3 + 4x2 - 7x - 10; (x - 2)
What is y = (x + 5)(x + 1)(x − 2)?
Solve by Graphing.
x4 - 2x3 - 5x2 + 1 = 0
What are x= {−1.33, −0.52, 0.42, 3.43} ?