By factorising, sketch the graph $y = 40 + x^2 - 13x$, showing the points of intersection with the coordinate axes.
$(x-5)(x-8)$, intercepts: $x=5,8$, $y$-intercept: $(0,40)$
By factorising, sketch the graph $y = x^2 - 2x - 63$, showing the points of intersection with the coordinate axes.
$(x-9)(x+7)$, intercepts: $x=-7,9$, $y$-intercept: $(0,-63)$
By factorising, sketch the graph $y = x^2 + 22x + 121$, showing the points of intersection with the coordinate axes.
$(x+11)^2$, intercepts: $x=-11$ (double root), $y$-intercept: $(0,121)$
By factorising, sketch the graph $y = 6x + x^2 - 72$, showing the points of intersection with the coordinate axes.
$(x+12)(x-6)$, intercepts: $x=-12,6$, $y$-intercept: $(0,-72)$
By factorising, sketch the graph $y = x^2 - 1$, showing the points of intersection with the coordinate axes.
$(x+1)(x-1)$, intercepts: $x=-1,1$, $y$-intercept: $(0,-1)$
By factorising, sketch the graph $y = 9x^2 - 16$, showing the points of intersection with the coordinate axes.
$(3x+4)(3x-4)$, intercepts: $x=-\tfrac{4}{3}, \tfrac{4}{3}$, $y$-intercept: $(0,-16)$
By factorising, sketch the graph $y = 2x^2 + 3x + 1$, showing the points of intersection with the coordinate axes.
$(2x+1)(x+1)$, intercepts: $x=-1,-\tfrac{1}{2}$, $y$-intercept: $(0,1)$
By factorising, sketch the graph $y = 2 + 7x + 3x^2$, showing the points of intersection with the coordinate axes.
$(3x+1)(x+2)$, intercepts: $x=-\tfrac{1}{3},-2$, $y$-intercept: $(0,2)$
By factorising, sketch the graph $y = -x^2 + 5x + 14$, showing the points of intersection with the coordinate axes.
$-(x-7)(x+2)$, intercepts: $x=7,-2$, $y$-intercept: $(0,14)$
By factorising, sketch the graph $y = -x^2 - 4x + 5$, showing the points of intersection with the coordinate axes.
$-(x+5)(x-1)$, intercepts: $x=-5, 1$, $y$-intercept: $(0,5)$
By factorising, sketch the graph $y = -2x^2 + 7x + 4$, showing the points of intersection with the coordinate axes.
$-(2x+1)(x-4)$, intercepts: $x=- frac{1}{2}, 4$, $y$-intercept: $(0,4)$
By factorising, sketch the graph $y = -3x^2 - 6x + 9$, showing the points of intersection with the coordinate axes.
$-3(x+3)(x-1)$, intercepts: $x=-3, 1$, $y$-intercept: $(0,9)$
Solve $2x^2 - 5x + 3 = 0$.
$x = 1,\; \tfrac{3}{2}$
Solve $2 - x - x^2 = 0$.
$x = -2,\; 1$
Solve $3x^2 - 2x - 1 = 0$.
$x = -\tfrac{1}{3},\; 1$
Solve $5 - 19x - 4x^2 = 0$.
$x = -5,\; \tfrac{1}{4}$
Solve $(x-2)(x+5)(x+1) = 0$.
$x = -5,\; -1,\; 2$
Solve $x^2(x-1)(x+1) = 0$.
$x = -1,\; 0,\; 1$
Solve $x - 6 + \dfrac{5}{x} = 0$.
$x = 1,\; 5$
Solve $\dfrac{x-6}{x-4} = x$.
$x = 2,\; 3$
Solve $(x-3)(x+1) = 5$.
$x = -2,\; 4$
Solve $x^3 - 2x^2 - 15x = 0$.
$x = -3,\; 0,\; 5$
Solve $2x^4 + 5x^3 - 3x^2 = 0$.
$x = \tfrac{1}{2},\; 0,\; -3$
Solve $6x^3 + x^2 - 2x = 0$.
$x = -\tfrac{2}{3},\; 0,\; \tfrac{1}{2}$
Fully factorise $x^4 - 5x^2 + 6$
$(x^2-2)(x^2-3)$
Fully factorise $x^6 + 7x^3 + 12$
$(x^3+3)(x^3+4)$
Fully factorise $x^4 - 9$
$(x^2-3)(x^2+3)$
Fully factorise $2x^4 + 7x^2 + 3$
$(2x^2+1)(x^2+3)$
Fully factorise $3x^5 - 5x^3 - 2x$
$x(3x^2+1)(x^2-2)$
Fully factorise $6x^6 - 2x^4 - 20x^2$
$x^2(3x^2+5)(2x^2-4)$
Factorise and solve $x^4 - x^2 - 12 = 0$
$(x^2 + 3)(x^2 - 4) \Rightarrow x = \pm 2$
Factorise and solve $-x^4 + 3x^2 - 2 = 0$
$(x^2 - 1)(2 - x^2) \Rightarrow x = \pm 1, \pm\sqrt{2}$
Factorise and solve $(x+3)^2 - (x+3) - 6 = 0$
$(x+3 + 2)(x+3 - 3) \Rightarrow x = -5, 0$
Factorise and solve $2^{2x} - 4\times 2^x = 0$
$2^x(2^x - 4) \Rightarrow x = 2$
Factorise and solve $3^{2x} - 10\times 3^x + 9 = 0$
$(3^x - 1)(3^x - 9) \Rightarrow x = 0, 2$
Factorise and solve $x - 9\sqrt{x} + 8 = 0$
$(\sqrt{x} - 1)(\sqrt{x} - 8) \Rightarrow x = 1, 64$
Factorise and solve $4^x + 2^x - 2 = 0$
$(2^x - 1)(2^x +2) \Rightarrow x = 0$
Factorise and solve $4^x + \times2^{x+1} - 8 = 0$
$(2^x - 2)(2^x + 4) \Rightarrow x = 1$
Factorise and solve $2^{2x+1} - 3\times2^x - 2 = 0$
$(2\times 2^x + 1)(2^x - 2) \Rightarrow x = 1$
Factorise and solve $3^{2x+1} - \times3^x - 2 = 0$
$(3\times3^x + 2)(3^x - 1) \Rightarrow x = 0$