Unit 7: Polynomials

 

  1. Calculate quotient and the remainder of the division P(x):Q(x)

P(x) = 4x5 – 6x4 + 2x2 + 8

 

Q(x) = x2 -2x -1

 

  1. Solve the following division with Ruffini’s Theorem, calculating the quotient and the remainder.

P(x) = 2x3 + 6x2 -3x -1

 

Q(x) = x + 3

  

  1. Demuestra que alguno de estos números: 2; -2 es raiz del siguiente polinomio:

P(x) = 3x3 – 6x2 +12x -24

 

(Use the Remainder Theorem)

 

  1. Calculate the remainder using the proper theorem:

P(x) = 2x3-4x2+5 entre x-3

 

  1. Find out the value of k in order to have P(x) divisible by x-2

P(x) = x3 – 5x2 + kx + 8

 

  1. Factorize the following polynomial:

a)x2+2x                b)x2+6x+9            c)x2-4x+4             d)x2-4

 

  1. Halla las raices y los factores de los siguientes polinomios:

a) x3 – 2x2 – 5x + 6

b) x3 – 5x2 + 7x – 3

c) x4 – 9x2 + 4x + 12

d) x4 – 8x3 + 14x2 + 8x -15

 

  1. Use the Ruffini’s Theorem to calculate P(-2), P(3) and P(5) in this cases:

a) P(x) = x4-3x3-x2+7x-2

b)P(x) = 2x3-7x2-16x+5

c) P(x) = 2x4-4x3-3x2+9x

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