Decide the factorization of the polynomial m2+5m+mt+5t

Question

Yusuf Keller · Accepted Answer

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

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

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