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Algebra Difficulty 2.5 Junior Find the answer Canada

For some integers $m$ and
$n$ , the expression $(x+m)(x+n)$ is equal to a quadratic
expression in $x$ with a constant
term of $-12$ . Which of the following
cannot be a value of $m$ ?

Pick one

Solution

Expanding, $(x+m)(x+n) = x^2 + nx + mx
+ mn = x^2 + (m+n)x + mn$.

The constant term of this quadratic expression is $mn$ , and so $mn
= -12$.

Since $m$ and $n$ are integers, they are each divisors of
$-12$ and thus of $12$ .

Of the given possibilities, only $5$ is not a divisor of $12$ , and so $m$ cannot equal $5$ .

We can check that each of the other four choices is a possible value of
$m$ .

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.