![\"\"](\"/images/stars/stars-13.gif\")
You can put this solution on YOUR website!
The first thing to do is to check the x^2 term and make sure that its coefficient (multiplier)
\n" ); document.write( "is 1. In this problem it is, so you can proceed.
\n" ); document.write( ".
\n" ); document.write( "Next look at the coefficient (multiplier) of the x term. That coefficient is -4. Then the
\n" ); document.write( "rule is to divide that by 2, square that, and add that result to the binomial you were originally
\n" ); document.write( "given. The result will be a perfect-square trinomial. Let's do it.
\n" ); document.write( ".
\n" ); document.write( "Start with the multiplier of the x term. That multiplier is -4. Divide it by 2 and you get
\n" ); document.write( "an answer of -2. Square the -2 and you get +4. Add that to the original binomial you were
\n" ); document.write( "given and it becomes:
\n" ); document.write( ".
\n" ); document.write( "x^2 - 4x + 4
\n" ); document.write( ".
\n" ); document.write( "And this is the perfect-square trinomial you were to find.
\n" ); document.write( ".
\n" ); document.write( "Notice that this can be factored as follows:
\n" ); document.write( ".
\n" ); document.write( "x^2 - 4x + 4 = (x - 2)(x - 2) = (x-2)^2
\n" ); document.write( ".
\n" ); document.write( "How can you easily tell what the factors will be? They will be x followed by half of the
\n" ); document.write( "original multiplier of the x term in the binomial ... in this case x followed by half of
\n" ); document.write( "the -4 that multiplied the x term. So the factors are both (x - 2).
\n" ); document.write( ".
\n" ); document.write( "Hope this gives you some insight into the process of making a perfect-square trinomial
\n" ); document.write( "when you are given the first two terms that involve x^2 and x.
\n" ); document.write( ".
\n" ); document.write( " \n" ); document.write( "