Question

Consider the rational expression x2+6x−2/6x−5 .

Which statements are true about the rational expression?

Select each correct answer.

Answer 1

Answer:

The last three terms are true.

Step-by-step explanation:

The last three statements are true.  Yes, the numerator has 3 terms:  x^2 + 6x - 2.  Yes, the denominator has 2 terms:  6x - 5.  Yes, that denominator is a single factor.

No, the numerator does not have three factors.  It does, however, have three terms.  No, 6x in the numerator does not cancel out the 6x in the denominator.

Answer 2

Answer:

Correct choices are C, D and E

Step-by-step explanation:

Consider expression $\dfrac{x^2+6x-2}{6x-5}.$

Note that numerator $x^2+6x-2$ consists of three terms: $x^2,\ 6x,\ -2$ and the denominator $6x-5$ consists of two terms: $6x,\ -5.$

A. False option.

The term in the numerator and in the denominator can be divided out, if both numerator and denominator are factored. Since $6x$ is a term in numerator and denominator and is not a factor, then it cannot be divided out.

B. False option.

The numerator is quadratic trinomial. Each quadratic trinomial has at most 2 factors. Since 3>2, then the numerator cannot have three factors.

C. True option, because three terms of the numerator are $x^2,\ 6x,\ -2.$

D. True option, because two terms of the denominator are $6x,\ -5.$

E. True option. The linear polynomial is always single factor.