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

Note: Actually, the division problem should be in reverse order. It should be given as $(x^{2} +3x+2) / (x+1)$ ---------(i)

But according to the given problem (x + 1) / (x² + 3 x + 2).

Here, (x² + 3 x + 2) > (x + 1)

or, (x + 2) > 1

Concept: By using the property of division, if the numerator is less than the denominator then the quotient will always be 0 (zero)

Therefore the option (d) 0 will be the correct option.

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..!!