Use polynomial division to simplify $$\dfrac{x^3+2x^2-x-2}{x+1}$$
$x^2+x-2$
Use polynomial division to simplify $$\dfrac{20+x+3x^2+x^3}{x+4}$$
$x^2-x+5$
Use polynomial division to simplify $$\dfrac{x^3-2x+21}{x+3}$$
$x^2-3x+7$
Use polynomial division to simplify $$\dfrac{3x^3+16x^2+72}{x+6}$$
$3x^2-2x+12$
Fidn the quotient and the remainder of $$\dfrac{x^3+8x^2+17x+16}{x+5}$$
Quotient: $x^2+3x+2$, Remainder: $6$
Fidn the quotient and the remainder of $$\dfrac{-x^3-5x^2+15x-50}{x+8}$$
Quotient: $-x^2+3x-9$, Remainder: $22$
Fidn the quotient and the remainder of $$\dfrac{4x^3+2x^2-16x+3}{x-3}$$
Quotient: $4x^2+14x+26$, Remainder: $81$
Fidn the quotient and the remainder of $$\dfrac{1-22x^2-6x^3}{x+2}$$
Quotient: $-6x^2-10x+20$, Remainder: $-39$
Use the factor theorem to determine whether $x-3$ is a factor of $$x^3-x^2-14x+27$$
No
Use the factor theorem to determine whether $x+6$ is a factor of $$2x^3+13x^2+2x-24$$
Yes
Use the factor theorem to determine whether $2x+1$ is a factor of $$2x^3-5x^2+7x-14$$
No
Use the factor theorem to determine whether $3x-2$ is a factor of $$2-17x+25x^2-6x^3$$
Yes
Show that $(x-1)$ is a factor of $$x^3-2x^2-11x+12$$ and hence write it as a product of three linear factors.
$(x-1)(x+3)(x-4)$
Given that $(x+3)$ is a factor, solve $$2x^3+x^2-13x+6=0$$
$x = -3, 0.5, 2$
Given that $x=-2$ is a solution to $$x^3+7x^2+7x-6=0$$ find, to 2 decimal places, the other two solutions.
$-5.54, 0.54$
Given $(x-2)$ is a factor of $$2x^3-x^2-15x+c$$ where $c$ is a constant, fully factorise it.
$(x-2)(2x-3)(x+3)$
$$\mathrm{f}(x) = 2x^3 + kx^2 - x + 6$$ Given that $(x+1)$ is a factor of $\mathrm{f}(x)$, find $k$ and hence fully factorise $\mathrm{f}(x)$.
$k = -5$ and $(x+1)(x-2)(2x-3)$
Given $(x+1)$ and $(x-3)$ are factors of $$x^3+px^2-13x+q$$ where $p$ and $q$ are constants, solve the equation $$x^3+px^2-13x+q = 0$$
$-5, -1, 3$
Given that $(x+2)$ and $(x-3)$ are factors of $$x^3-5x^2+ax+b$$ express it as a product of three linear factors.
$(x+2)(x-3)(x-4)$
Given that $(x-2)$ is a factor of $$3x^3-x^2-12x+4$$ solve the equation $$3x^3-x^2-12x+4 = 0$$
$-2, \dfrac{1}{3}, 2$