L3 Complex Numbers
Question Bank
Find the remainder when $3x^3 + 2x^2 - 7x + 4$ is divided by $(x + 2)$.
$(x - 4)$ is a factor of $x^3 - 5x^2 + kx + 8$, where $k$ is a real constant.
Find the value of $k$.
$(x + 3)$ is a factor of $p(x) = 2x^3 + 5x^2 - 4x + k$, where $k$ is a real constant.
Find the value of $k$.
When $2x^3 + kx^2 - 5x + 1$ is divided by $(x - 3)$, the remainder is $4$.
Find the value of the real constant $k$.
Find the remainder when the polynomial $P(x) = 2x^3 - 4x^2 + 5x - 3$ is divided by $(x - 2)$.
$(x - 3)$ is a factor of $x^3 - kx^2 + 2kx - 9$, where $k$ is a real constant.
Find the value of $k$.
Given that $(3x + 2)$ is a factor of $3x^3 + kx^2 - 7x - 6$, find the value of $k$.
When $p(x) = 2x^4 - 7x^2 + kx + 3$ is divided by $(x + 2)$, the remainder is $1$.
Find the value of the real constant $k$.
The polynomial $P(x) = x^3 + kx^2 - 5x + 6$ has $(x - 3)$ as a factor.
Find the value of $k$.
$f(x) = 2x^3 + ax^2 + bx - 3$, where $a$ and $b$ are real constants.
When $f(x)$ is divided by $(x - 1)$ the remainder is $-4$, and when $f(x)$ is divided by $(x + 2)$ the remainder is $-7$.
Find the values of $a$ and $b$.
The polynomial $p(x) = 2x^3 + ax^2 + bx - 4$ has $(2x + 1)$ as a factor. When $p(x)$ is divided by $(x - 2)$, the remainder is 10.
Find the values of $a$ and $b$.
$p(x) = 2x^3 + ax^2 + bx + 6$, where $a$ and $b$ are real constants.
$(x + 3)$ is a factor of $p(x)$, and when $p(x)$ is divided by $(x + 1)$ the remainder is $18$.
Find the values of $a$ and $b$, and hence factorise $p(x)$ fully.
The polynomial $P(x) = x^3 + ax^2 + bx + 6$ has $(x - 2)$ as a factor.
When $P(x)$ is divided by $(x + 1)$, the remainder is 6.
Find the values of $a$ and $b$.