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ANSWERS: 3
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No. That's it.
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Yes, if you are allowed to use complex numbers. It would be (a+bi)(a-bi). This is easy to verify, just remember that i*i=-1. With complex numbers, any polynomial can be reduced to a product of first degree polynomials. Not so if you are allowed to use real numbers only.
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9-11-2017 A big part of math is pattern recognition. A lot of homework is just fighting with stuff so you will remember the pattern when you see it again. The most common pattern is (x + a) * (x + b) = x^2 + (a + b)x + ab and the special case (x + a) * (x - a) = x^2 - a^2. When you spot the pattern you can just write the answer from memory. Now study this page until it seems obvious: en.wikipedia.org/wiki/Polynomial_remainder_theorem The given equation is an example of "difference of squares" and the factor is then (a + bi)(a - bi).
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