Write the polynomial in descending powers of the variable and with no missing powers. 4y+3y^4

Question

stuck on this question, Thankyou!!

Answer 1

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 + 3y⁴ . The two terms here are +4y and +3y⁴ . 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 3y⁴ .

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: 0y³ , 0y² , 4y, which is the power of y¹, and finally y⁰ if we include that power.

The final answer would be 3y⁴ + 0y³ + 0y² + 4y + 0y⁰ .

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. :)

Answer 2

Put the highest degree first

3y^4 + 4y

That would seem to be the normal preferred answer, unless you want to list every explicit power, then:

3y^4 + 0y^3 + 0y^2 + 4y +0

the cubic, quadratic and constant terms are all 0, or you can put in the actual powers with 0 coeffients:

3y^4 + 0y^3 + 0y^2 +4y^1 + 0y^0

y is the same as y raised to the 1 power

a constant term such as 0 is the same as 0 times y to the zero power. Anything to the zero power = 1, and 0 times 1 = 0

Listing every degree 0 to 4 may show you understand degrees more than just the conventional 3y^4+4y, but it's not recommended unless the instructor or textbook is specially asking for that. When you say "no missing powers' perhaps that's what they want, all of them, with 0 coefficients.