Factor the polynomial ?
I need to factor completely. Is my answer right?
2x³+4x²+10x+20
=2x²(x+2)+10(x+2)
=(2x²+10)(x+2)
=2(x²+5)(x+2)
=2(x+i√5)(x−i√5)(x+2)
If this is incorrect, please correct me.
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I need to factor completely. Is my answer right?
2x³+4x²+10x+20
=2x²(x+2)+10(x+2)
=(2x²+10)(x+2)
=2(x²+5)(x+2)
=2(x+i√5)(x−i√5)(x+2)
If this is incorrect, please correct me.
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Answers & Comments
Your answer is correct.
The question is ambiguously worded. You should get full marks because your intermediate steps include the results of factoring completely over the real numbers. Your final answer factors completely over the irrational and complex numbers. So you have covered all possible interpretations of the question.
When you get a badly worded question like this, it worth erring on the cautious side and supplying the extra level of working.
Unless told to factor over complex or irrational numbers, I'd stop at:
2(x² + 5)(x + 2)