# Evaluate the remainder of division of $P(x)$ by $x^2 - 4x$.

When a polynomial $$P(x)$$ is divided by $$x^2 - 3x$$, the quotient and remainder are $$Q(x)$$ and $$2x-8$$ respectively. The remainder of division of $$Q(x)$$ by $$x-4$$ is $$2$$. Evaluate the remainder of division of $$P(x)$$ by $$x^2 - 4x$$.

From linear division of polynomials, one can conclude that

$$Q(4) = 2$$

I also obtained that

$$P(3) = Q(x)(2x-8)$$

This is where I'm stuck. Could you assist me?

Regards

• I will translate the conditions into equations. You have $Q(x)=R(x)(x-4)+2$ for some $R(x)$ unknown polynomial. You have $P(x)=(x^2-3x)Q(x)+2x-8$. Can you solve it from here? – Alec B-G Feb 6 at 16:21
• Anyone cannot help with that? – Enzo Feb 6 at 21:58
• I'll write a bit more $P(x)=x(x-4)(x-3)R(x)+2(x^2-3x)+2x-8$. – Alec B-G Feb 7 at 12:37