Victor S. answered • 02/18/20

Math, Science, & Test Prep Instructor with 11+ years coaching students

Hi Brooke,

We can translate these mathematical terms into their meanings and translate those into symbols on the page.

First, the polynomial ("many terms") is 4y + 3y^{4} . The two terms here are +4y and +3y^{4} . I'm emphasizing they're both positive.

Next, "descending powers of the variable" means starting with the term of the highest power and write the remaining terms in descending order, or greatest to least.

We start with the term 3y^{4 }.

Next, "no missing powers" means we'll write more "y" terms with the 3rd, 2nd, and 1st powers.

Since there are no terms provided, how do we write "placeholder" y terms?

We use zero as a coeffecient for those terms.

The next y terms are: 0y^{3} , 0y^{2} , 4y, which is the power of y^{1}, and finally y^{0 }if we include that power.

The final answer would be 3y^{4} + 0y^{3} + 0y^{2} + 4y + 0y^{0} .

It may seem that the 0 coefficient terms are unnecessary. We often track polynomials in precalc and calculus before finding the derivative or integral. Polynomials are always best written in descending order of the powers of the terms. :)