Find a 4 degree polynomial having zeros -6,-3,2 and 6 and the coefficient of x^4 equal 1

The "coefficient of x^4 equal 1" is really throwing me off.

Thanks.

1 answer

a x ^ 4 + b x ^ 3 + c x ^ 2 + d x + e =

a ( x - x1 ) * ( x - x2 ) * ( x - x3 ) * ( x - x4 )

In your case:

a = 1

So:

x ^ 4 + b x ^ 3 + c x ^ 2 + d x + e =

( x - ( - 6 ) ) * ( x - ( - 3 ) ) * ( x - 2 ) * ( x - 6 ) =

( x + 6 ) * ( x + 3 ) * ( x - 2 ) * ( x - 6 ) =

x ^ 4 + x ^ 3 - 42 x ^ 2 -36 x + 216