Maths F.5 Trigonometry

1(a) x^3 + 2x^2 + 4x + 3 = (x + 1)(x^2 + x + 3)

as x^2 + x + 3 do not have a linear factor => x+1 is the only linear factor of x^3 + 2x^2 + 4x +3

(b) Let x = 2cosy

x^3 + 2x^2 + 4x + 3 = 0

8(cosy)^3 + 8(cosy)^2 + 8cosy + 3 = 0

2cosy + 1 = 0 or 4(cosy)^2 + 2cosy + 3 = 0

As 2^2 - 4(4)(3) < 0, the second equation does not have a reaal root

So, cosy = -1/2 and y = 120 or 240