Answer: -4g^4 - 3g^3 + 4g^2 + 5g + 3
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Work Shown:
Something like g^2 means "g squared"
(g^2 - 4g^4 + 5g + 9) + ( -3g^3 + 3g^2 - 6)
g^2 - 4g^4 + 5g + 9 - 3g^3 + 3g^2 - 6
-4g^4 - 3g^3 + (g^2 + 3g^2) + 5g + (9-6)
-4g^4 - 3g^3 + 4g^2 + 5g + 3
Note that g^2 and 3g^2 are one pair of like terms that combine to 4g^2. It might help to think of g^2 as 1g^2. The other pair of like terms are 9 and -6 which combine to 3.
Convention is to write the polynomial with the largest exponent term first, followed by the term with the next largest exponent, and so on. This is called standard form.