Question

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

Answer 1

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.

Answer 2

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.