Question

Consider the rational expression.

6x+12x2+8x+12
Which statements are true?

Select each correct answer.




12 is a term in both the numerator and denominator.

x + 2 is a factor of the numerator.

2 is a common factor in the numerator and denominator.

The denominator has 3 terms.

Answer 1

The options 1,2 and 4 are correct.

Explanation:

The given rational expression

`(6x+12)/(x^2+8x+12)`

From the given expression it is noticed 12 is a term in both the numerator and denominator. Option 1 is correct.

The denominator has 3 terms. Option 4 is correct.

`(6(x+2))/(x^2+6x+2x+12)`

`(6(x+2))/(x(x+6)+2(x+6))`

`(6(x+2))/((x+6)(x+2))`

From the above expression it is clear that (x+2) is a factor of the numerator. Option 2 is correct.

Therefore options 1,2 and 4 are correct.