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To factorise an expression such as x ² - 8x + 15, you need to look for two numbers that add up to make -8 and multiply to give 15.
The only option in this case is -5 and -3
(-5)+(-3)=...

Split into partial fractions: (3x +2) / (x² - 5x +6) = A / (x-3) + B / (x-2) => 3x + 2 = A(x-2) + B(x-3) let x =...

Use product rule i.e. (uv)'=u'v+uv'Set u=e^x and differentiate to find u'=e^x Set v=cosx and differentiate to find v'=-sinxTherefore (uv)' where uv=e^xcosx =e^xcosx + e^x(-sinx)=e^xcosx - e^xsinx=e^x(cosx...

I already done this.

Remember that the equation of a line is y=mx+c and m is the gradient of the line. The gradient of a perpendicular line will be the negative reciprocal of m ( that just means it will be -1/m). You can then...