## Tuesday, May 24, 2016

### Daily Regents: Functions and Multiplying Polynomials

I'll be reviewing a New York State Regents Exam Question every day from now until the Regents exams begin next month. At least, that is the plan.

### August 2014, Questions 27 and 28

27. Guy and Jim work at a furniture store. Guy is paid \$185 per week plus 3% of his total sales in dollars, x, which can be represented by g(x) = 185 + 0.03x. Jim is paid \$275 per week plus 2.5% of his total sales in dollars, x, which can be represented by f(x) = 275 + 0.025x. Determine the value of x, in dollars, that will make their weekly pay the same.

To find the value of x where both functions are the same, you can set them each to each other, and solve the equation.

g(x) = f(x)
185 + 0.03x = 275 + 0.025x
185 + 0.005x = 275
0.005x = 90
x = 90/0.005 = 18,000

If they both have sales of \$18,000, their salaries will be equal.

If you want to check, put 18,000 into each function. Both will give you \$725.

28. Express the product of 2x2 + 7x - 10 and x + 5 in standard form.

Use the Distributive Property. Then combine like terms, writing the terms starting with the highest exponent and going in descending order.

(x)(2x2 + 7x - 10) + (5)(2x2 + 7x - 10)
2x3 + 7x2 - 10x + 10x2 + 35x - 50
2x3 + 17x2 + 25x - 50

Any questions?

If anyone in Brooklyn is looking for an Algebra or Geometry Regents Prep tutor, send me a note. I have a couple of weekly spots available between now and June.