Herramientas informaticas

jueves, 15 de octubre de 2015

Multiplying polynomials


To multiply polynomials, follow these steps:
P(x) = 2x2 − 3    Q(x) = 2x3 − 3x2 + 4x


1. Multiply all monomials from the first polynomial by all of the monomials in the second polynomial.
P(x) ·  Q(x) = (2x2 − 3) · (2x3 − 3x2 + 4x) =
= 4x5 − 6x4 + 8x3 − 6x3 + 9x2 − 12x =

2.Add the monomials of the same degree:
= 4x5 − 6x4 + 2x3 + 9x2 − 12x

The multiplication of polynomials is another polynomial whose degree is the sum of the degrees of the polynomials.
Also, polynomials can be multiplied as follows:


 







Example 
 
Multiply the polynomials using two different methods:
P(x) = 3x4 + 5x3 − 2x + 3 and Q(x) = 2x2 − x + 3
P(x) · Q(x) = (3x4 + 5x3 − 2x + 3) · (2x2 − x + 3) =
= 6x6 − 3x5 + 9x4 + 10x5 − 5x4 + 15x3
− 4x3 + 2x2 − 6x + 6x2 − 3x + 9 =
= 6x6 + 7x5 + 4x4 + 11x3 + 8x2 − 9x + 9




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