Algebra 2 Problems of the Day

Algebra 2 is not my usual subject, but I do get asked about the problems occasionally. So I've decided to run a couple of Regents problems daily for a while. If there's a positive reaction (or at least, a lack of negative reaction), I may continue it.

More Algebra 2 problems.

January 2018
9. What is the quotient when 10x³ - 3x² - 7x + 3 is divided by 2x - 1?

(1) 5x² + x + 3
(2) 5x² - x + 3
(3) 5x² - x - 3
(4) 5x² + x - 3

Answer: (4) 5x² + x - 3
First of all, if you divide +3 by -1, the result must be -3, so we can eliminate choices (1) and (2).
Since it's multiple choice, it might be easier just to multiply the two remaining choices by 2x - 1 to see which one works. As they only differ by one sign, it should be quick to do, as shown in the image below:

As you can see, +x gives you +2x², which when added to the -5x² in the first column, makes a total of -3x². So the correct answer is choice (4).

If you wanted to divide (after eliminating the two bad choices), 2x - 1 goes into (10x³ - 3x²), 5x² times.
(10x³ - 3x²) - (10x³ - 5x²) = 2x²
Bring down the next term, -7x. At this point, you will notice that 2x goes into (2x²), +x times, not -x times. You now have enough information to answer the question.



10. Judith puts $5000 into an investment account with interest compounded continuously. Which approximate annual rate is needed for the account to grow to $9110 after 30 years?

(1) 2%
(2) 2.2%
(3) 0.02%
(4) 0.022%

Answer: (1) 2%
You can check each rate to see which gives you $9110 after 30 years, or you can work backward to solve it.
Use the Continuously Compounded Interest formula A = Pe^rt
9100 = 5000e^30r
(9100/5000) = e^30r
ln(9100/5000) = ln(e^30r)
ln(9100/5000) = 30r
ln(9100/5000)/30 = r
r = 0.0199978..., which is approximately 0.02, or 2%.



Comments and questions welcome.