To find the polynomial resulting from the subtraction [tex]\( N - T \)[/tex], we start by defining the polynomials [tex]\( T \)[/tex] and [tex]\( N \)[/tex]:
[tex]\[ T = -2a^2 + a + 6 \][/tex]
[tex]\[ N = -3a^2 + 2a - 5 \][/tex]
We need to subtract [tex]\( T \)[/tex] from [tex]\( N \)[/tex]:
[tex]\[ N - T = (-3a^2 + 2a - 5) - (-2a^2 + a + 6) \][/tex]
To perform the subtraction, we distribute the negative sign across the terms in [tex]\( T \)[/tex]:
[tex]\[ N - T = -3a^2 + 2a - 5 + 2a^2 - a - 6 \][/tex]
Next, we combine like terms:
- Combine the [tex]\( a^2 \)[/tex] terms:
[tex]\[ -3a^2 + 2a^2 = -1a^2 \][/tex]
- Combine the [tex]\( a \)[/tex] terms:
[tex]\[ 2a - a = 1a\][/tex]
- Combine the constant terms:
[tex]\[ -5 - 6 = -11 \][/tex]
Therefore, the resulting polynomial from the subtraction [tex]\( N - T \)[/tex] is:
[tex]\[ -a^2 + a - 11 \][/tex]
So, the polynomial in its standard form is:
[tex]\[ N - T = -a^2 + a - 11 \][/tex]
