Question

Question 1

(i) If (x + 3) is a factor of the
expression x^3 + 3x^2 - x - 3, find the other two factors?

(ii) If the expression above was divided by (x + 2), what is the remainder?

Answer 1

$(i)\;\;\frac{x^3+3x^2-x-3}{x+3}=\frac{x^3+3x^2}{x+3}-\frac{x+3}{x+3}=x^2-1=(x+1)(x-1)$

So, other two factors: $x+1$ and $x-1$

(ii) $(-2)^3+3*(-2)^2-(-2)-3=3.$

Remainder is 3.