Question

the polynomial 3x+5 is divided by x+2 what is the quotient, pls be quick im taking a algebra progress check due in 25 min

Answer 1

Answer:

The quotient of the rational function is $3 -\frac{1}{x+2}$.

Step-by-step explanation:

We proceed to solve the expression by solely algebraic means below:

1) $\frac{3\cdot x + 5}{x+2}$ Given

2) $\frac{(3\cdot x + 5) + 0}{x + 2}$ Modulative property

3) $\frac{(3\cdot x +5) + [1+(-1)]}{x+2}$ Existence of additive inverse/Associative property

4) $\frac{(3\cdot x + 6)+(-1)}{x+2}$ Definition of addition/Commutative and associative properties

5) $\frac{3\cdot (x+2)}{x+2} + \left(-\frac{1}{x+2} \right)$   $\frac{a+b}{c} = \frac{a}{c} + \frac{b}{c}$/ $\frac{-a}{b} = \frac{a}{-b} = -\frac{a}{b}$/Distributive property

6) $3 -\frac{1}{x+2}$ Definition of division/Existence of multiplicative inverse/Modulative property/Definition of subtraction/Result

The quotient of the rational function is $3 -\frac{1}{x+2}$.