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Get Full Access to CU - MATH 1150 - Class Notes - Week 2
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CU / Math / MATH 1150 / What are the functions of polynomials?

# What are the functions of polynomials? Description

##### Description: These notes cover chapter B.3, and include polynomials, and how to add, subtract, multiply, and divide them.
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B.3 PolynomialsWe also discuss several other topics like Where does carbohydrates come from?

1. Expression of the form
• anXn + an-1 Xn-1 + ...a2X2 + a1X + a0
• Where n EN or n = 0, an0 if n0, and ai ER. n is the degree, and the leading coefficient an, and ao is constant

**Example: 5x2 - x + 3x4 -2

• Degree = 4
• Constant = 2

• Degree is largest power of x = n
• coefficient are R in front of x
• Leading is R in front of largest power of x
• Constant is R with no x terms
• Non - polynomials
• , 1/x, log x, sinx, etc
1. Operations (+, - x, )
• Example: (3x3 - x - 2) + (2x3 - 7x2 + 4x)
• 5x3 - 7x2 + 3x - 2
• Subtract like terms
• Example: (3x3 - x - 2) - (2x3 - 7x2 + 4x)
• = x3 + 7x2 - 5x - 2
• Multiply
• Multiply every term
• Example: (3x2)(2x3 - 7x2 + 4x) - = 6x6 - 21x5 + 6x4 + 21x3 -12x2
• Foil
• (a+b)(c+d) = ac + ad + bc + bd
• (a+b) (a-b) = a2 - b2
• (a+b)2 = a2 + 2ab + b2
• (a-b)2) = a2 - 2ab - b2
• Divide
• Example: (3x3 - x2 - 9x + 6) (quotient)

(x2+3)(3x5 - x4 + 3x2 + x-5)We also discuss several other topics like How do we use rational expressions?

-3x5 (-9x3)

-x4 - 9x3 + 3x2 + x - 5

+x4        + 32Don't forget about the age old question of 7pi/9

-9x3 + 6x2 + x - 5

+x4        + 3x2If you want to learn more check out What is the process by which a division of labor occurs as different workers specialize in tasks?

-9x3 + 6x2 + x - 5

-6x2        -18We also discuss several other topics like What is the definition of a quotient rules?
If you want to learn more check out How many forms of equation are there?

(Remainder) - (28x - 23)

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