Question

What is the quotient of the following division problem (x+ 1)÷(x^2 + 3x +2)

a.x+ 2
b.x +1
c.x^2 +3x +2
d. 0

Answer 1

The quotient of the division problem (x + 1) ÷ (x^2 + 3x + 2) is 0 since the numerator is of lower degree than the denominator and cannot be divided evenly without leaving a remainder.

Step-by-step explanation:

The student asked what the quotient of the division problem (x + 1) ÷ (x^2 + 3x + 2) would be. To simplify a fraction where the numerator is of lower degree than the denominator as in this case, we know that the quotient will not contain any variable terms, as the numerator cannot be divided by the denominator to result in a polynomial. The quotient is simply 0, since there is no value of x that would allow x + 1 to be divided by x^2 + 3x + 2 without leaving a remainder, unless we are considering the division in the context of rational expressions, where the quotient would remain as the entire fraction itself. However, based on the options provided and understanding the context as a simple division to find the polynomial quotient, the correct answer is 0.

Answer 2

We have to find the quotient of the following division problem (x+ 1)÷(x^2 + 3x +2)

Actually, the question should be the inverse of the given fraction i.e., (x^2 + 3x +2 ) / (x +1)

So, the dividend is (x^2 + 3x + 2) and Divisor is (x +1)

Now, let's factorise the dividend as follow:

x^2 + 3x + 2

= x^2 + 2x +x + 2

= x ( x + 2) + 1 ( x + 2)

= (x +1)(x + 2)

So the given fraction becomes (x + 1)(x + 2) / (x + 1)

Hence the quotient is (x + 2)

Hope this helps..!!