Question

If f(x)=x^2+3x+1 and g(x)=x+1 find the quotient and remainder if the polynomial f(x) is divided by g(x).

Answer 1

Answer:

$\large \boxed{\sf \ \ \ \dfrac{f(x)}{g(x)}=x+2-\dfrac{1}{x+1} \ \ \ }$

Step-by-step explanation:

Hello,

$f(x)=x^2+3x+1\\\\g(x)=x+1\\\\\boxed{x}(x+1)=x^2+x \ \text{ and } \ \ f(x)-x(x+1)=2x+1\\\\\boxed{2}(x+1)=2x+2 \ \ \text{ and } \ \ 2x+1-2x-2=\boxed{-1} \ \ \text{so }\\\\f(x)=\boxed{(x+2)}(x+1)\boxed{-1} \ \ \text{ then }\\\\\dfrac{f(x)}{g(x)}=x+2-\dfrac{1}{x+1}$

Quotient is x + 2

Remainder is -1

Hope this helps.

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Thank you