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

Question
Polynomial factorization
asked 2021-02-20
Decide the factorization of the polynomial \(m^{2}+5m+mt+5t\)

Answers (1)

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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