Question 1
The polynomial $\text{f}\left( x \right)$ of degree $3$ leaves a remainder of $10$ when divided by $x-2$ and $-15$ when divided by $x+3$. Find the remainder of $\text{f}\left( x \right)$ when it is divided by ${{x}^{2}}+x-6$.
Question 2
The expressions ${{x}^{3}}-2{{x}^{2}}-3x-11$ and ${{x}^{3}}-{{x}^{2}}-9$ leave the same remainder when divided by $x+a$.
Find
(i)
the two possible values of $a$,
(ii)
the larger of the two corresponding remainders.
(i)
(ii)
Question 3
If ${{x}^{3}}-h{{x}^{2}}+kx-9$ has a factor of ${{x}^{2}}+3$, find $h$ and $k$ and the other factor.
Question 4
2018 SNGS MYA Q5
The term containing the highest power of $x$ in the polynomial $\text{f}\left( x \right)$ is $2{{x}^{3}}$. The roots of the equation $\text{f}\left( x \right)=0$ are $-1$, $1$ and $k$. The polynomial $\text{f}\left( x \right)$ has a remainder of $-48$ when divided by $x-3$.
(i)
Find the value of $k$.
[3]
(ii)
Find the remainder when $\text{f}\left( x \right)$ is divided by $x$.
[1]
(iii)
Sketch the graph of $y=\text{f}\left( x \right)$.
[2]
(i)
(ii)
(iii)
Question 5
2018 SNGS MYA Q7
The function $\text{f}\left( x \right)=2{{x}^{4}}+p{{x}^{3}}+q{{x}^{2}}+19x-15$ is exactly divisible by $2{{x}^{2}}+5x-3$.
(i)
Find the value of $p$ and of $q$.
[6]
(ii)
Show that the equation $2{{x}^{4}}+p{{x}^{3}}+q{{x}^{2}}+19x-15=0$ has only two real roots.
[3]
(i)
(ii)
