Question

Factor each polynomial. If a polynomial cannot be factored, write prime. Factor out the greatest common factor as necessary: m^{2}-5m-14

Polynomial factorization
ANSWERED
asked 2021-06-08
Factor each polynomial. If a polynomial cannot be factored, write prime. Factor out the greatest common factor as necessary:
\(m^{2}-5m-14\)

Answers (1)

2021-06-09

Step 1
We have to factor the polynomial:
\(m^{2}-5m-14\)
Factorizing by middle term splitting method,
Here,
\(14=7\times 2\)
and middle term can be replaced as:
\(-7+2=-5\)
Therefore,
\(m^{2}-5m-14=m^{2}-7m+2m-14=mm-7+2m-7\)
Step 2
Taking common \(m-7\), we get
\(mm-7+2m-7=m-7m+2\)
Hence, factor of the polynomial is \(m-7m+2\).
Here greatest factor is \(m+2\) since m is increased by 2 but in \(m-7\), m is decreased by 7.

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