Since they are not like terms (not the same variables) you cannot simply so you leave it like that.✨ This applies for addition and subtraction only. It’s different with multiplication and division.✨
If the roots to such a polynomial are 2 and
, then we can write it as
courtesy of the fundamental theorem of algebra. Now expanding yields
which would be the correct answer, but clearly this option is not listed. Which is silly, because none of the offered solutions are *the* polynomial of lowest degree and leading coefficient 1.
So this makes me think you're expected to increase the multiplicity of one of the given roots, or you're expected to pull another root out of thin air. Judging by the choices, I think it's the latter, and that you're somehow supposed to know to use
as a root. In this case, that would make our polynomial
so that the answer is (probably) the third choice.
Whoever originally wrote this question should reevaluate their word choice...
Remember that the formula for simple interest is:
- is the interest earned
- is the principal amount invested
- is the interest rate, represented as a decimal
- is the amount of time in years
Using information the problem gave us, we can say that the amount of interest earned after one year is:
After 1 year, we will have earned $21. Remember though that we also need to find the amount we will earn after 4 months. Since there are 12 months in a full year, we can say that 4 mohts represents a third of a year. Thus, let's multiply our interest by one-third.
After 4 months, we will have generated $7 and after one year we will have generated $21.