Answer
Fill the blanks with
$(x+3)\quad$ and $\quad 6$
Work Step by Step
By the division algorithm, when dividing polynomials $f(x)\div g(x)$
we obtain a quotient $q(x)$ (with lesser degree than $g(x)$ )
and a remainder $r(x)$
such that
$f(x)=g(x)\cdot q(x)+r(x)$
In this case,
$(x^{2}+2x+3)=(x-1)\underbrace{(x+3)}_{q(x)}+\underbrace{6}_{r(x)}$
Fill the blanks with
$(x+3)\quad$ and $\quad 6$
