Answer:
x² + 2x + 3
Step-by-step explanation:
given [tex]\frac{x^3+3x^2+5x+3}{x+1}[/tex]
One way of dividing is to use the divisor as a factor in the numerator
Consider the numerator
x²(x + 1) - x² + 3x² + 5x + 3
= x²(x + 1) + 2x(x + 1) - 2x + 5x + 3
= x²(x + 1) + 2x(x + 1) + 3(x + 1) - 3 + 3
= x²(x + 1) + 2x(x + 1) + 3(x + 1) + 0
[tex]\frac{x^3+3x^2+5x+3}{x+1}[/tex]
= [tex]\frac{(x+1)(x^2+2x+3)}{x+1}[/tex] = x² + 2x + 3 ← quotient
