Question

Find a polynomial of the specified degree that satisfies the given conditions.

Degree 4; zeros −1, 0, 5, 1/5

coefficient of x3 is 21

Answer 1

Answer: -x(x+1)(x-5)(5x-1)

Explanation:

According to the zeroes given by the question

x = -1,0,5,1/5

The f(x) must contain

x(x+1)(x-5)(5x-1) = 5x^4 - 21x^3 - 21x^2 +5x

But the question wanted the coefficient of the x^3 to be +21

So, we multiply negative into the function

-x(x+1)(x-5)(5x-1)