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

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.