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x^3 + 2x^2 - 9x - 18 = (x^2 - a^2)(x + b) where a,b are integers. Work out the three linear factors of x^3 + 2x^2 - 9x - 18. (Note: x^3 indicates x cubed and x^2 indicates x squared).

There are a few different ways to approach this problem. The most obvious is to attempt to factorise x 3 + 2x 2 - 9x - 18. However it is very difficult to approach the problem like this. fortunately the ques...
CB
5131 Views

Factorise 6x^2 + 7x + 2

6x^2 + 7x + 2 can be written in the form ax^2 + bx + c. In order to factorise this I use the following method which can be used to factorise similar equations. Multiply 'a' and 'c' to get ac (here this is 6 ...
HP
14478 Views

By using an integrating factor, solve the differential equation dy/dx + 4y/x = 6x^-3 (6 marks)

Answer : y = 3/x 2 + c/x 4 Integrating factor is 4/x (1 mark) => I = e integral (4/x) dx (1 mark) => I = x 4 (1 mark) . Using the formula, d/dx (x 4 y) = 6x (1 mark) => x 4 y = integral(6x)dx (1 mar...
MD
7231 Views

I don't understand how proof by mathematical induction works, can you help?

This took me some time to get my head around so I know what you mean. I always like to think of proof by induction like dominoes. Once you've pushed the first domino in line of dominos, you know it's going t...
JB
2790 Views

Solve the following complex equation: '(a + b)(2 + i) = b + 1 + (10 + 2a)i' to find values for 'a' and 'b'

The first step with this question is to expand all the brackets; this will produce the following equation: 2a + ai + 2b + bi = b + 1 + 10i + 2ai The next step is to put all the terms which contain what you'r...
SM
15728 Views