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Unformatted text preview: r a 2 out of the first term to get, 4 x 2 + 10 x  6 = 2 ( 2 x  1) ( x + 3) This is exactly what we got the first time and so we really do have the same factored form of this
polynomial.
[Return to Problems] © 2007 Paul Dawkins 37 http://tutorial.math.lamar.edu/terms.aspx College Algebra Special Forms
There are some nice special forms of some polynomials that can make factoring easier for us on
occasion. Here are the special forms. a 2 + 2ab + b 2 = ( a + b ) 2 a 2  2ab + b 2 = ( a  b ) 2 a 2  b 2 = ( a + b )( a  b ) a 3 + b3 = ( a + b ) ( a 2  ab + b 2 )
a 3  b3 = ( a  b ) ( a 2 + ab + b 2 ) Let’s work some examples with these. Example 4 Factor each of the following.
(a) x 2  20 x + 100 [Solution]
(b) 25 x 2  9 [Solution]
(c) 8 x3 + 1 [Solution]
Solution
(a) x 2  20 x + 100
In this case we’ve got three terms and it’s a quadratic polynomial. Notice as well that the
constant is a perfect square and its square root is 10. Notice as well that 2(10)=20 and this is the
coefficient of the x term. So, it looks like we’ve got the second special form above. The correct
factoring of this polynomial is, x 2  20 x + 100 = ( x  10 ) 2 To be honest, it might have been easier to...
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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
 MrVinh

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