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Since there is an x^2 term, we know that there are two brackets that are of the form (x-) (x-), but we need to fill in the blanks! What are the two numbers where you can add them up to make 3, an...

f(-1) = (-1)^3 - (-1)*7 - 6 = -1 + 7 - 6 = 0

Hence f(x) = (x+1)(x^2 + ax - 6)

Expand this out

f(x) = x^3 + ax^2 - 6x + x^2 + ax - 6 

      = x^3 + (a+1)x^2 + (a-6)x -6

B...

Mathematical induction is a type of direct proof, where you can prove sequences or series. A good example of this is that we can prove 1 + 3 + 5 + .... + (2n-1) = n^2. There are 4 steps: 1. Prove the firs...

The longest straight line within the cuboid is the diagonal from a corner to the corner diagonally from it (show diagram), call this D. So to find out whether the pole will fit, find this length, if it is...

f(x) = cx + d f(0) = c0 + d = d = -6 => d = -6 f(2) = c2 + d = c2 + -6 = 10 => c2 - 6 = 10 => c = (10 + 6) / 2 => c = 8