Remainder Theorem.md

• Relationship of degree of terms in remainder theorem

---

Here since we take quotient as Q(x) as it really doesn't matter and the remainder as Ax +B cuz when any degree 3 polynomial is divided by a degree 2 polynomial the remainder should be linear. Then we get 2 equations and subject what you dont know which A and B respectively. Then we substitute the values that we were given eariler to show what we are asked.

---

In here, since we don't know the Q(x) we can ignore it and use it like this. When a 4th degree polynomial is divided by a linear factor, the remainder should be 3rd degree. Therefore, we can get the remainder as ax^2 + bx +c for now and derive simultaneous equations like this.

---

In here, normally what we would do is to get the f(x) as $Ax^4+Bx^3+9x^2+Cx+D$ and then try to apply remainder theorem. But since they have already given that $(x-2)^2$ is a factor, we can write f(x) as $(x-2)^2(Ax^2 + Bx + C)$. This way, the number of variables we have to find becomes less.