MAths help...?

Question

The curves y= 2x^3 and y=(2-x)(5x+6) intersect in three points. find the x coordinates of this point...u can use cubic equation formula...
The remainder when 2x^3 + 9x^2 + 7x +3 is divided by x - k . Find k.

Answer 1

1) y = 2x^3 and y = (2 - x)(5x + 6)

Therefore, 2x^3 = (2 - x)(5x + 6)

So, 2x^3 + 5x^2 - 4x - 12 = 0

Trying factors (x ± 1), (x ± 2), (x ± 3) and (x ± 6),
it is found to factor as (2x - 3)(x + 2)^2 = 0.

Thus the zeros are x = 3/2 and a double point at x = -2.

2) The remainder by synthetic division is :
2k^3 + 9k^2 + 7k + 3,
but you don't say what it equals, so I can't calculate k.