Factoring Polynomials: (x-3)(x+5)=x^2+2x-15

John Whitaker

Junior Member
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May 9, 2006
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In a Chapter on Factoring Polynomials, my book shows an equation:

. . .(x - 3)(x + 5) = x^2 + 2x - 15

To the right of the equal sign, I don't understand where the "2x" comes from. I read this as (x)(x) and (-3)(+5).
What am I missing?
Thank you.
John Whitaker
 
\(\displaystyle \L
\begin{array}{rcl}
\\
\left[ {x - 3} \right]\left( {x + 5} \right) & = & \left[ {x - 3} \right](x) + \left[ {x - 3} \right](5) \\
& = & \left[ {x^2 - 3x} \right] + \left[ {5x - 15} \right] \\
& = & x^2 + 2x - 15 \\
or \\
\left[ {x - 3} \right]\left( {x + 5} \right) & = & \left[ {x\left( {x + 5} \right) - 3(x + 5)} \right] \\
& = & \left[ {x^2 + 5x - 3x - 15} \right] \\
& = & x^2 + 2x - 15 \\
or \\
\left( {x - 3} \right)\left( {x + 5} \right) & = & x^2 + ( - 3 + 5)x - 15 \\
\end{array}\)
 
(x - 3)(x + 5)
Put 'em one under the other, and multiply each term left to right:
x - 3
x + 5
=========
x^2 - 3x
.........5x - 15
=========
x^2 + 2x - 15
 
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