Question

What is the quotient (x3 + 3x2 + 5x + 3) ÷ (x + 1)?

x2 + 4x + 9
x2 + 2x
x2 + 2x + 3
x2 + 3x + 8

Answer 1

Hello,

Answer C

x^3+3x²+5x+3=x^3+2x²+3x + x²+2x+3=x(x²+2x+3)+1(x²+2x+3)=(x²+2x+3)(x+1)

Answer 2

Answer: The correct option is (C)
`x^2+2x+3.`

Step-by-step explanation: We are given to find the quotient by dividing the following :

`Q=(x^3+3x^2+5x+3)/(x+1).`

We will try to factorize the numerator ad then divide by the denominator to find the quotient.

We have

`Q\\\\\\=(x^3+3x^2+5x+3)/(x+1)\\\\\\=(x^2(x+1)+2x(x+1)+3(x+1))/(x+1)\\\\\\=((x+1)(x^2+2x+3))/((x+1))\\\\=x^2+2x+3.`

Thus, the required quotient is
`x^2+2x+3.`

Option (C) is correct.