Math CentralQuandaries & Queries


Question from eddie, a teacher:


Hi Eddie,

I expect you are to factor this expression. Since all the signs are positive the challenge is to find integers $a, b, c \mbox{ and }d$ so that

\[2x^2+5x+2 = (ax + b)(cx + d).\]

When you expand the right side the first term is $a \times bx^2$ so $a \times b = 2.$Thus one of $a$ and $b$ is 2 and the other is 1. Likewise the constant term is $b \times d$ and hence $b \times d$ is 2 and thus one of $b$ and $d$ is 2 and the other one is 1.

Can you find a choice of $a, b, c \mbox{ and }d$ so that the middle term is $5x?%


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