Unformatted text preview: ce we know that
x = 2 is a zero of P ( x ) and we get any other number than zero in that last entry we will know
that we’ve done something wrong and we can go back and find the mistake.
Now, let’s get back to the problem. From the synthetic division we have, P ( x ) = ( x - 2 ) ( x 2 + 4 x + 3) So, this means that, Q ( x ) = x2 + 4x + 3 and we can find the zeroes of this. Here they are, Q ( x ) = x 2 + 4 x + 3 = ( x + 3) ( x + 1) Þ x = -3, x = -1 So, the three zeroes of P ( x ) are x = -3 , x = -1 and x = 2 .
As a aside to the previous example notice that we can also now completely factor the polynomial
P ( x ) = x3 + 2 x 2 - 5 x - 6 . Substituting the factored form of Q ( x ) into P ( x ) we get, P ( x ) = ( x - 2 ) ( x + 3) ( x + 1)
This is how the polynomials in the first set of examples were factored by the way. Those require
a little more work than this, but they can be done in the same manner. © 2007 Paul Dawkins 254 http://tutorial.math.lamar.edu/terms.aspx College Algebra Graphing Polynomials
In this secti...
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This note was uploaded on 06/06/2012 for the course ICT 4 taught by Professor Mrvinh during the Spring '12 term at Hanoi University of Technology.
- Spring '12