To find the resulting polynomial when we add the polynomials [tex]\( M \)[/tex] and [tex]\( T \)[/tex] together, let's break down each step carefully.
Firstly, let's write down the given polynomials:
[tex]\[
M = -8r^2 + 11r - 6
\][/tex]
[tex]\[
T = -7r^2 - 9r + 14
\][/tex]
Next, we need to add these two polynomials together by combining like terms. Let's start by adding the coefficients of the [tex]\( r^2 \)[/tex], [tex]\( r \)[/tex], and constant terms separately.
1. Combining the [tex]\( r^2 \)[/tex] terms:
[tex]\[
-8r^2 + (-7r^2) = -15r^2
\][/tex]
2. Combining the [tex]\( r \)[/tex] terms:
[tex]\[
11r + (-9r) = 2r
\][/tex]
3. Combining the constant terms:
[tex]\[
-6 + 14 = 8
\][/tex]
Now, we combine all these results to form the new polynomial:
[tex]\[
M + T = -15r^2 + 2r + 8
\][/tex]
So, the polynomial in standard form is:
[tex]\[
\boxed{-15r^2 + 2r + 8}
\][/tex]
