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(2+2x^2+4x)/(x^2+3x+2)

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2 Answers

Carol B. is absolutely right.

Notice that when you factor a trinomial (a polynomial with three terms), you are performing a puzzle of sorts.  You have to ask, "What are two numbers that when added together give me [the coefficient in front of x], but when multiplied give me [the non-variable term], in this case, 2 and 1 in the numerator, and  3 and 2 in the denominator.

You can recognize the pattern better when you rewrite the polynomial in standard form as Carol has done above, with the highest exponents first and the lowest exponents last. This will make the factoring easier and may have been what tripped you up when trying to solve the problem.

Notice that you can factor a 2 from the numerator to get

[2(x^2 + 2x +1)]/(x^2 + 3x +2)

Next, we factor both numerator and denominator to get

[2(x+1)(x+1)]/(x+1)(x+2)

Cancelling (x+1) from both numerator and denominator gives

[2(x+1)]/(x+2)