Question

A polynomial P(x) has real number coefficients and zeros 0, 3, and x. Write an expression for P(x) in standard form with the lowest possible degree and the leading coefficient equal to 1.

a) P(x) = x^3 - 3x^2
b) P(x) = x^3 - 3x
c) P(x) = x^3 + 3x^2
d) P(x) = x^3 + 3x

Answer 1

The polynomial P(x) with zeros 0, 3, and x, a leading coefficient of 1, and the lowest degree is
`P(x) = x^3 - 3x^2`, represented by option a).

Step-by-step explanation:

To write an expression for the polynomial P(x) with zeros 0, 3, and x, and with a leading coefficient of 1, we consider that the polynomial will be the product of the factors corresponding to each zero. Since zero is a zero of the polynomial, one factor is x.

For the zero at 3, the corresponding factor is (x - 3).

For the zero at x, we just have x again as a factor.

Combining these results, the polynomial will be P(x) = x(x)(x - 3).

Simplifying this expression gives us
`P(x) = x^3 - 3x^2`, which is represented by option a).