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

Question

1687 views around the world

You can reuse this answer
Creative Commons License

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!