Add the Proper Constant to Each Binomial So That the Resulting

question 68

Multiple Choice

Add the proper constant to each binomial so that the resulting trinomial is a perfect square trinomial. Then factor the
trinomial.
- $x ^ { 2 } - \frac { 2 } { 11 } x +$ ____

• A) \(x ^ { 2 } - \frac { 2 } { 11 } x + \frac { 1 } { \underline { 121 } } = \left( x + \frac { 1 } { 11 } \right) ^ { 2 }\)
• B) \(x ^ { 2 } - \frac { 2 } { 11 } x + \frac { 2 } { 121 } = \left( x - \frac { 1 } { 11 } \right) ^ { 2 }\)
• C) \(x ^ { 2 } - \frac { 2 } { 11 } x + \frac { 1 } { \underline { 121 } } = \left( x - \frac { 1 } { 11 } \right) ^ { 2 }\)
• D) \(x ^ { 2 } - \frac { 2 } { 11 } x + \frac { 4 } { 121 } = \left( x - \frac { 2 } { 11 } \right) ^ { 2 }\)

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Definitions:

Doublet

A pattern, especially in spectroscopy, where a signal is split into two components with a small separation, indicating the interaction between nuclear spins.

Multiplet

A pattern in NMR spectroscopy composed of closely spaced spectral lines, indicating the presence of coupling between nuclear spins.

Fourier Transform NMR

A technique in nuclear magnetic resonance spectroscopy that uses the Fourier transform principle to convert time domain data into frequency domain data, offering detailed information on molecular structure.

Continuous Wave

A form of radiation or signal that maintains a constant amplitude and frequency over time.