How do you write a polynomial with zeros 1,-4,5 and leading coefficient 1?

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Answer 1 · 2016-10-15T13:50:53

The equation is #y = x^3 - 2x^2 - 19x + 20#

A polynomial in factored form, is written as #y = a(x - a)(x - b)(x- c)...# where #a, b, c, ...# are the zeroes and #a# is the leading coefficient.

Hence, we can write the polynomial function as

#y = 1(x - 1)(x + 4)(x - 5)#

If you want this in standard form, simply multiply out.

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

#y = x^3 + 3x^2 - 4x - 5x^2 - 15x + 20#

#y = x^3 - 2x^2 - 19x + 20#

Hopefully this helps!