document.write( "Question 587930: X2+x-(a+2)(a+1)=0 \n" ); document.write( "

Algebra.Com's Answer #374313 by KMST(5328) $\"\"$ $\"About$

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$\"x2%2Bx-%28a%2B2%29%28a%2B1%29=0\"$
\n" ); document.write( "If you had $\"x2%2B%28b%2Bc%29x%2Bbc=0\"$ (it would be confusing if I used a),
\n" ); document.write( "you would factor to solve and have
\n" ); document.write( " $\"%28x%2Bb%29%28x%2Bc%29=0\"$ with solutions $\"x=-b\"$ and $\"x=-c\"$
\n" ); document.write( "The constant (independent term) in a quadratic (degree 2) polynomial is the product of the constants (independent terms) of the factors.
\n" ); document.write( "The coefficient of the term is x is the sum of those same factors.
\n" ); document.write( "The trick to factoring is to find the pair of factors for the constant that add to the coefficient of the term is x.
\n" ); document.write( "The constant in your equation is $\"+-%28a%2B2%29%28a%2B1%29\"$
\n" ); document.write( "The coefficient of x in your equation is 1, and
\n" ); document.write( " $\"1=%28a%2B2%29-%28a%2B1%29\"$
\n" ); document.write( "So your factors are $\"a%2B2\"$ and $\"-%28a%2B1%29\"$ .
\n" ); document.write( "Your quadratic polynomial factors like this:
\n" ); document.write( " $\"x2%2Bx-%28a%2B2%29%28a%2B1%29=%28x%2B%28a%2B2%29%29%28x-%28a%2B1%29%29\"$
\n" ); document.write( "Your equation is equivalent to
\n" ); document.write( " $\"%28x%2B%28a%2B2%29%29%28x-%28a%2B1%29%29=0\"$
\n" ); document.write( "and the solutions are
\n" ); document.write( " $\"x=a%2B1\"$ and $\"x=-%28a%2B2%29=-a-2\"$ \n" ); document.write( "

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