Algebra 2 Problems of the Day (Algebra 2/Trigonometry Regents, January 2012)

Now that I'm caught up with the current New York State Regents exams, I'm revisiting some older ones.

More Regents problems.

Algebra 2/Trigonometry Regents, January 2012

Part IV: Each correct answer will receive 6 credits. Partial credit is available.


36. Perform the indicated operations and simplify completely:

(x³ - 3x² + 6x - 18) / (x² - 4x) * (2x = 4) / (x⁴ - 3x³) ÷ (x² + 2x - 8) / (16 - x²)

Answer:

First, change the division to multiplication and replace the last fraction with its inverse (i.e., "flip it", replace it with its reciprocal). Then, factor everything that can be factored. Finally, cancel out the common factors.

In particular, the first numerator can be factored by grouping. The last numerator (after flipping) is the Differenc of Two Perfect Squares. However, (16 - x²) can be reversed by multiplying by -1, becoming -1(x² - 16), which will be easier to work with.

What remains will be -2(x² + 6) / x⁴. You can multiply the two factors in the numerator, or leave them separate. Both are acceptable.

End of Exam.

More to come. Comments and questions welcome.

More Regents problems.

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