# Decide the factorization of the polynomial m^{2}+5m+mt+5t

Question
Polynomial factorization
Decide the factorization of the polynomial $$m^{2}+5m+mt+5t$$

2021-02-21
Formula used:
The factors of a polynomial can be find by taking a common factor and this method is called factor by grouping,
$$ab+ac+bd+cd=a(b+c)+d(b+c)$$
$$=(a+d)(b+c)$$
Or,
$$ab - ac + bd-cd = a(b-c)+d(b-c)$$
$$= (a+d)(b-c)$$
Calculation:
Consider the polynomial $$m^{2} + 5m + mt + 5t$$.
This is a four term polynomial, factorization of this polynomial can be find by factor by grouping as,
$$m^{2} + 5m + mt + 5t = (m^{2} + Sm) + (mt + 5t)$$
$$=m(m+5)+t(m+5)$$
As, $$(m + 5)$$ is the common factor of the polynomial factor it out as follows:
$$m^{2} + 5m + mt + 5t = (m + 5m) + (mt + 5t)$$
$$=m(m+5)+t(m+5)$$
$$=(m+5)(m+1)$$
The factorization of the polynomial $$m^{2} + 5m + mt + 5t$$ is $$(m+5)(m+t)$$.
Check the result as follows:
$$(m+5)(m+t})=m*m+m*t+5*m+5*t$$
$$=m^{2}+mt+5m+5t$$
$$=m^{2}+5m+mt+5t$$
Thus, the factorization of the polynomial $$m^{2} + 5m + mt + 5t$$ is $$(m+5)(m+t)$$.

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