Write a polynomial as the sum of the monomials and write it in standard form. for each of the above specify the degree of the resulting polynomial. 4a, −5b·b^2, −3c, +7b^3, +c, −2a, 1

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