Question

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

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 :

$Q=\dfrac{x^3+3x^2+5x+3}{x+1}.$

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

We have

$Q\\\\\\=\dfrac{x^3+3x^2+5x+3}{x+1}\\\\\\=\dfrac{x^2(x+1)+2x(x+1)+3(x+1)}{x+1}\\\\\\=\dfrac{(x+1)(x^2+2x+3)}{(x+1)}\\\\=x^2+2x+3.$

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

Option (C) is correct.