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Solve the following problem:

[tex]\[
\begin{array}{l}
T = -2a^2 + a + 6 \\
N = -3a^2 + 2a - 5
\end{array}
\][/tex]

Find [tex]\( N - T \)[/tex].

Your answer should be a polynomial in standard form.

Sagot :

GinnyAnswer
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]
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