Add, Multiply, Classify
Write the polynomial in standard form. Identify the degree and leading coefficient of the polynomial. Then classify the polynomial by the number of terms:
\pi r^2 - \frac{5}{7}r^8 + 2r^5
-\frac{5}{7}r^8 + 2r^5 + \pi r^2
A degree-8 trinomial with leading coefficient -\frac{5}{7}
Factor the polynomial:
3z^2 - 27
3(z + 3)(z - 3)
Sofia has once again been caught chewing gum in class. In a moment of panic, Sofia accidentally launches her gum into the air. The gum’s height, in feet, can be modeled by the equation
h = -16t^2 + 104t + 56.
How many seconds will it take for the gum to hit the ground?
7 seconds.
Solve the equation:
9k^2 + 66k = -21
k = -\frac{1}{3}, k = -7
Find the difference:
(-y^2 + y + 2) - (y^2 - 5y - 2)
-2y^2 + 6y + 4
Factor the polynomial:
9y^2 + 6y - 8
(3y + 4)(3y - 2)
Daniel and Eddie are preparing for a guitar performance. They load a crate full of guitar accessaries into a helicopter and drop it from a height of 1600 feet. The height of the crate, in feet, can be modeled by the equation
h = -16t^2 + 1600.
How long will it take for the crate to crash-land.
10 seconds.
Solve the equation:
k^4 - 100k^2 = 0
k = 0, k = \pm 10
Find the sum:
(x^2 + 6x - 5) + (2x^2 + 15)
3x^2 + 6x + 10
Factor the polynomial:
2a^2 - 12b + 8ab - 3a
(2a - 3)(a + 4b)
Garen just finished building a birdhouse in the shape of a rectangular prism with volume 128 cubic inches. The width of the birdhouse is w inches, the length is 4 inches, and the height is 4 inches greater than the width. What are the dimensions of the birdhouse?
length: 4 in
width: 4 in
height 8 in
Solve the equation:
x^3 + x^2 = 4x + 4
x = -1, x = \pm 2
Divide the polynomials:
\frac{3x^2 - 12x - 15}{x - 5}
3(x + 1)
For what values of t can
2x^2 + tx + 10
be written as the product of two binomials with integer coefficients and constants?
\pm 9, \pm 12, \pm 21
Ariana and Loreni are designing square picture frames for each of their classmates.
The area (in square centimeters) of each frame can be represented by
d^2 + 8d + 16.
Write an expression that represents the perimeter of the frame in centimeters.
4d + 16
Solve the equation for q in terms of p:
q^2 + q + 5pq + 5p = 0
-1, -5p