1Is the equation \( 5x^3 - 6x^2 + 7x - 6 = 0 \) satisfied when \( x = 1 \)?
2How can the factors of \( 5x^3 - 6x^2 + 7x - 6 \) be found?
3What are the factors of \( 5x^3 - 6x^2 + 7x - 6 \)?
4Test whether 1, \( -1 \), \( -2 \), 2, \( -3 \) and 3 are roots or zeros of \( f(x) = x^3 - 6x^2 + 11x - 6 \), and find its factors.
5Find the polynomial \( f(x) \) whose zeros are 2, 4 and 6.
6Factorise: \( x^3 + 6x^2 + 11x + 6 \)
7Factorise: \( x^3 - 3x^2 - 4x + 12 \)
8Factorise: \( x^3 - 8x^2 + 19x - 12 \)
9Factorise: \( (x + 2)(x^2 - 11x + 48) - 120 \)
10Factorise: \( (x - 3)(3x^2 - 10x + 2) - 10 \)
11Solve: \( x^3 - 3x^2 - 10x + 24 = 0 \)
12Solve: \( 2x^3 + 3x^2 - 11x - 6 = 0 \)
13Solve: \( x^3 + 26x = 9x^2 + 24 \)
14Solve: \( x^3 - 4x^2 = 17x - 60 \)
15Solve: \( (x + 4)(x^2 - x - 14) + 16 = 0 \)
16Solve: \( (x - 3)(3x^2 - 10x + 2) = 10 \)
17Explain why 5 cannot be a root of \( x^3 - x^2 - 10x - 8 = 0 \), without substituting it.
18List the possible rational roots of \( 3x^3 - 4x^2 - 5x + 2 = 0 \), then solve the equation.
19Factorise \( x^3 - 13x - 12 \).