Introduction to Polynomials
What is the coefficient of the following expression:
3x2y3
3
Identify the like terms in this set:
5y, xy, -y, 4x, y2
5y and -y
2(y-7)
= 2y - 14
In a hockey tournament, teams are awarded 3 points for a win, 2 points for an overtime win, and 1 point for an overtime loss.
Define your variables and then write an expression that describes the number of points a team has.
Let o represent number of points for overtime wins
Let l represent number of points for overtime loss
Total points = 3w + 2o + l
What type of polynomial is the following expression?
a + 2b + c - 1
4 term polynomial
Identify the like terms in the following set:
3a2b3, -2b3a2, 2a2b, ab
3a2b3, -2b3a2
- 4b (b +2)
= -4b2 - 8b
A rectangular window frame has dimensions expressed by 3x and 2x-5
Write a simplified expression for the area of the frame.
A = l x w
A = 3x (2x - 5)
A = 6x2 - 15x
How many terms are in this expression and what type of polynomial is it?
x2 + 3x + 2
3 and trinomial
(4x + 3) + (3x + 2)
= 4x + 3 + 3x + 2
= 4x + 3x + 3 + 2
= 7x + 5
−3𝑥(2𝑥2 − 5𝑥 + 4)
= −3𝑥(2x2) − (−3𝑥)(5𝑥) + (−3𝑥)(4)
= −6𝑥3 + 15𝑥2 − 12𝑥
Substitute and solve using values m = -2 and n = 5 in the expression: 5m2 - 3mn + 8n - 7m + 1
= 5 (-2)2 - 3(-2)(5) + 8(5) - 7(-2) + 1
= 5 (4) - 3 (-10) + 40 +14 +1
= 20 + 30 + 40 + 14 + 1
= 50 + 40 + 14 + 1
= 90 + 14 + 1
= 104 + 1
= 105
What degree of term is the following:
8
No degree; it's a constant
(2a2 - 4a - 2) - 3(a2 - 4a + 2)
= 2a2 - 4a - 2 - 3a2 + 12a - 6
= 2a2 - 3a2 - 4a + 12a - 2- 6
= - a2 + 8a - 8
3𝑚(𝑚 − 5) − (2𝑚2 − 𝑚)
= 3𝑚(𝑚) − (3𝑚)(5) − (2𝑚2) − (−𝑚)
= 3𝑚2 − 15𝑚 − 2𝑚2 + 𝑚
= 𝑚2 − 14𝑚
Determine a simplified expression for the perimeter of the composite shape.
Answer will be on board
What degree of polynomial is the following expression?
2/3x3y6 + z8
9
(6𝑥 − 12) − (−9𝑥 − 4) − (𝑥 + 14)
= 6𝑥 − 12 − (−9𝑥) − (−4) − 𝑥 − 14
= 6𝑥 − 12 + 9𝑥 + 4 − 𝑥 − 14
= 6𝑥 + 9𝑥 − 𝑥 − 12 + 4 − 14
= 14𝑥 − 22
−2[3𝑥−(4−2𝑦)]+5[𝑦−2(𝑥+1)]
= −2[3𝑥 − 4 − (−2𝑦)] + 5[𝑦 − 2(𝑥) + (−2)(1)]
= −2(3𝑥 − 4 + 2𝑦) + 5(𝑦 − 2𝑥 − 2)
= −6𝑥 + 8 − 4𝑦 + 5𝑦 − 10𝑥 − 10
= −16𝑥 + 𝑦 − 2
A cube has a volume of 125 cm3. Find the total surface area of all six faces.
Remember: Volume of a cube
Surface Area = Total area of all 6 faces
Area of one face= (length)(width).
Solution will be on board but answer is 150 cm3
s = 5 cm
A of one face = lxw
A = 5 cm x 5 cm
A of one face = 25 cm2