Answer:
2b³ +2a -2c . . . . degree 3 polynomial
Step-by-step explanation:
The monomials are ...
... 4a . . . . degree 1 in a
... -5b·b² = -5b³ . . . . degree 3 in b
... -3c . . . . degree 1 in c
... 7b³ . . . . degee 3 in b (like term with -5b³)
... +c . . . . degree 1 in c (like term with -3c)
... -2a . . . . degree 1 in a (like term with 4a)
So, we have 3 pairs of like terms. The like terms can be combined by summing their coefficients.
The degree of the polynomial is that of the highest-degree term. (Here, the b³ term makes it a polynomial of degree 3.)
... 4a -2a = (4-2)a = 2a . . . . combining the "a" terms
... -5b³ +7b³ = (-5+7)b³ = 2b³ . . . . combining the b³ terms
... -3c +c = (-3 +1)c = -2c . . . . combining the "c" terms
In standard form, we write the highest-degree term first. Follwing terms are in order by decreasing degree. It is convenient, but perhaps not required, to then write the terms of the same degree in alphabetical order.
... = 2b³ +2a -2c . . . . a 3rd degree polynomial
