Answer:
The factorized form of 4n^2 -5n-6 is (4n+3)(n-2)
Step-by-step explanation:
The simplest way to determine the correct factorized form is to expand the equation of each option. Remember:
(a+b)(c+d) =a.c + a.d + b.c + b.d
Let's calculate the expansion of each factortorized form:
[tex]A)\ (4n-3)(n+2) = 4(n).(n)+(4n)(2)+(-3)(n)+(-3).(2)[/tex]
[tex]= 4n^2+8n-3n-6[/tex]
[tex]= 4n^2+5n-6[/tex]
[tex]B)\ (4n+3)(n-2) = 4(n).(n)+(4n)(-2)+(3)(n)+(3).(-2)[/tex]
[tex]4n^2-8n+3n-6[/tex]
[tex]4n^2-5n-6[/tex]
[tex]C)\ (4n+2)(n-3) = 4(n).(n)+(4n)(-3)+(2)(n)+(2).(-3)[/tex]
[tex]=4n^2-12n+2n-6[/tex]
[tex]=4n^2-10n-6[/tex]
Note that all the option have the same qaudratic (4) and independent (-6) coefficents but only the options B have the same linear coefficents (-5).
