Question

Create a polynomial function in standard form with a leading coefficient of 2 and zeros at 0 1 and 3 brainly

Answer 1

Answer:

$P(x) = 2x^3 - 8x^2 + 6x$

Step-by-step explanation:

Given

$p =2$ -- Leading coefficient

$Zeros: 0, 1\ and\ 3$

Required

Determine the polynomial

Represent the zeros with a, b and c.

Such that

$a = 0$

$b = 1$

$c = 3$

The polynomial is:

$P(x) = p * (x - a) * (x - b) * (x - c)$

$P(x) = 2 * (x - 0) * (x - 1) * (x - 3)$

$P(x) = 2x * (x - 1) * (x - 3)$

Open bracket

$P(x) = (2x^2 - 2x) * (x - 3)$

$P(x) = 2x^3 - 6x^2 - 2x^2 + 6x$

$P(x) = 2x^3 - 8x^2 + 6x$