More Algebra 2 problems.

*January 2018, Part III*

Questions in Part II are worth 4 credits. All work must be shown or explained for full credit. A correct numerical answer without work is only worth 1 credit.

*33.Given: f(x) = 2x ^{2} + x - 3 and g(x) = x - 1
Express f(x) • g(x) - [f(x) + g(x)] as a polynomial in standard form.*

**Answer: **

f(x) • g(x) = (2x^{2} + x - 3)(x - 1)

= 2x^{3} - 2x^{2} + x^{2} - x - 3x + 3

= 2x^{3} - x^{2} - 4x + 3

[f(x) + g(x)] = (2x^{2} + x - 3) + (x - 1)

= 2x^{2} + 2x - 4

f(x) • g(x) - [f(x) + g(x)] = 2x^{3} - x^{2} - 4x + 3 - [2x^{2} + 2x - 4]

= 2x^{3} - x^{2} - 4x + 3 - 2x^{2} - 2x + 4

= **2x ^{3} - 3x^{2} - 6x + 7 **

*34. A student is chosen at random from the student body at a given high school. The probability that
the student selects Math as the favorite subject is 1/4. The probability that the student chosen is
a junior is 116/459. If the probability that the student selected is a junior or that the student chooses
Math as the favorite subject is 47/108, what is the exact probability that the student selected is a
junior whose favorite subject is Math?
*

*Are the events “the student is a junior” and “the student’s favorite subject is Math” independent
of each other? Explain your answer.
*

**Answer: **

Given: P(M) = 1/4, P(J) = 116/459, and P(M or J) = 47/108.

P(M and J) = P(M) + P(J) - P(M or J)

P(M and J) = 1/4 + 116/459 - 47/108 = 0.06753812636

Use the calculators convert to Fraction function (Math 1. >FRAC), and you get **31/459**.

If you didn't know how to convert to fraction on the calculator, then you needed to find a common denominator before doing all of the work. *A decimal answer is no good because the exact probability is required.*

The least common multiple of 459 and 108 is 1836, which is also divisible by 4. If you didn't know how to use the LCM function on the calculator, then you could have created tables of values for y = 108x and y = 459x to get all the multiples.

1/4 = 459/1836

116/459 = 464/1836

47/108 = 799/1836

(459 + 464 - 799) / 1836 = 124/1836 = 31/459.

If P(M) and P(J) are independent, then P(M) • P(J) = P(M and J)

(1/4)(116/459) ?= (31/459)

0.06318082788 =/= 0.06753812636

So the events are NOT independent.

Reminder: you need to *explain* something in words. You can't just show the multiplication (which is a "justification", but not an "explanation".)

Comments and questions welcome.

More Algebra 2 problems.

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