Adding/Subtracting Polynomials
(5x2 + 7x - 2x3)+(6x3-7x-2x2)
3x2 + 4x3
6v(2v+3)
12v2 + 18v
3x + 9y + 12z
3(x+3y+4z)
A rock is dropped from a 100 foot tower. The height of the rock as a function of time can be modeled using the vertical motion model. How long does it take the rock to reach the ground?
t = 10/4 seconds or 2.5 seconds
What is the degree and leading coefficient of the following problem: 7x3-3x4+6x2
Leading Coefficient: -3
Degree: 4
(z - 6z2 +8z4)+(z2 + 4z4)
z - 5z2 +12z4
(6p + 8)(5p - 8)
30p2 - 8p - 64
b2 + 8b + 7
(b + 7)(b - 1)
A soccer ball is kicked upward at an initial velocity of 60 ft/sec. How high is the ball off the ground at 1 second?
44 feet
What is the degree of the monomial: 4x6y5z
Degree: 12
(7-13x3-11x)-(2x3+8-4x5)
-4x5-15x3-11x-1
(2a - 1)(8a - 5)
16a2 - 18a + 5
m2 + m - 90
(m - 9)(m + 10)
A rectangle with a width of (x + 2) feet and a length of x feet has an area of 24 sq feet. What is the rectangles length and width?
Can the following polynomial be factored using a special pattern: 4x2 +6x + 9
If so, factor it.
Yes; (2x+3)2
15v5 + 4v3 - 24v2
(4a + 2)(6a2 - a + 2)
24a3 + 8a2 + 6a + 4
2(n + 9)(n - 6)
The area of a rectangle is 70 square inches. The length is one less than three times the width. What is the width of the rectangle?
Solve using a special pattern:
(5y - 10)(5y + 10)
25y2 - 100
(-9v2 - 8u) + (-2uv - 2u2 + v2) + (-v2 + 4uv)
-9v2 + 2uv - 2u2 - 8u
(4p - 1)2
16p2 - 8p + 1
x2 - 15x + 50
(x - 10)(x - 5)
While throwing a temper tantrum, an angry toddler standing on a chair screams and throws his ice cream cone into the air from 5 feet above the ground with an initial vertical velocity of 30 feet per second (he’s pretty strong!). How long does it take before the cone hits his baby brother’s head 1 foot above the ground?
2 seconds
f(x) = 169x2 - 225
x = 15/13 and x = -15/13