Find a degree 3 polynomial that has zeros 2 4 and 6 and in

Find a degree 3 polynomial that has zeros - 2, 4 and 6 and in which the coefficient of x^2 is -16.

Solution

degree 3 polynomial that has zeros - 2, 4 and 6

=>(x-(-2))(x-4)(x-6)

=>(x+2)(x-4)(x-6)

=>(x+2)(x²-10x+24)

=>x(x²-10x+24) +2(x²-10x+24)

=>(x³-10x²+24x) +(2x²-20x+48)

=>x³-10x²+24x +2x²-20x+48

=>x³-8x²+4x+48

given coefficient of x^2 is -16. so multiply by 2

=>2x³-16x²+8x+96

degree 3 polynomial that has zeros - 2, 4 and 6 and in which the coefficient of x^2 is -16 is 2x³-16x²+8x+96