document.write( "Question 1130114: List the characteristics of a perfect square quadratic. \n" ); document.write( "

Algebra.Com's Answer #746766 by MathLover1(20849) $\"\"$ $\"About$

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A perfect square is a quadratic expression that factors into two identical binomials.\r
\n" ); document.write( "\n" ); document.write( "To use this idea effectively, it is important that we learn to identify perfect square trinomials. Note that the ﬁrst and last terms of $\"x%5E2%2B14x+%2B49\"$ are perfect squares of $\"x\"$ and $\"7\"$ , and the middle term is twice the product of these two terms: $\"2+%2A+7=14\"$ . These are the characteristics of a perfect square trinomial. \r
\n" ); document.write( "\n" ); document.write( "If the coefficient is of the quadratic term is $\"1\"$ , take the coefficient of the linear term, divide it by $\"+2\"$ , and then square it.\r
\n" ); document.write( "\n" ); document.write( "Quadratic trinomials in standard form on the left have been converted to completed square form, and the completed square form is just the perfect square in factored form with some remainder constant tagged on at the end. \r
\n" ); document.write( "\n" ); document.write( "In general, to factor a quadratic trinomial of the form $\"ax%5E2%2Bbx%2Bc\"$ , find two integers, $\"m\"$ and $\"n\"$ , such that $\"mn=c+\"$ and $\"m+%2B+n+=+b\"$ . If such a pair of integers cannot be found,the trinomial is not factorable over the integers and it is described as prime.\r
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