Consider the rational expression 4x+5/3x^2+x+5 which statements are true about the rational expression? select each correct answer. a.) the numerator has two terms b.) the denominator has three terms c.) 5 in the numerator divides out with 5 in the denominator d.) the denominator has three factors e.) 3x^2 + x + 5 is a single factor in the denominator

Statement a, b are true.

Step-by-step explanation:

First we have to define term,

A term is any constant, variable, or product of constants and variables in an expression, typically separated by a + or - sign.

For statement a,

The numerator has two terms. One is 3x and the other is 5.

For Statement b,

The denominator has three terms. One is 3x^2, second is x and the third term is 5.

For Statement c,

The number 5 in both numerator and denominator is added to the other terms, it had to be a multiplicative factor in both to cancel out. So it cannot be cancelled out.

For Statement d,

The number of factors of a polynomial are equal to its degree. The denominator is a polynomial of degree two/Quadratic, so it will not have more than 2 factors. So statement d is false.

For Statement e

The denominator is not a single factor as it is a degree 2 polynomial which can be further broken down to 2 factors.

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step-by-step explanation:

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-12 -5(x + 4) = 3x

-12 - 5x - 20 = 3x

-12 - 20 - 5x = 3x

-32 - 5x = 3x

    + 5x   + 5x

-32 = 8x

8         8

- 4= x