$\left(7{x}^{2}-6x+6\right)+\left(3{x}^{3}-9x\right)$
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FieniChoonin
A polynomial in a variable x is a function of the form ${a}_{n}{x}^{n}+{a}_{n-1}{x}^{n-1}+\dots +{a}_{1}x+{a}_{0}$. This polynomial has degree n. The constants ${a}_{i}$ are the coefficients and are constants.
To add two polynomials we add like terms, that is, add terms of the same degree. For example $2{x}^{2},4{x}^{2}$ are terms of the same degree but the terms $2{x}^{2},4{x}^{3}$ are terms of different degree.
The sum to be computed is $\left(7{x}^{2}-6x+6\right)+\left(3{x}^{3}-9x\right)$. . Drop the parenthesis and combine like terms.
$\left(7{x}^{2}-6x+6\right)+\left(3{x}^{3}-9x\right)=7{x}^{2}-6x+3{x}^{3}-9x$
$=3{x}^{3}+7{x}^{2}+\left(-6x-9x\right)+6$
$=3{x}^{3}+7{x}^{2}-15x+6$
Hence, the sum is $3{x}^{3}+7{x}^{2}-15x+6$.