Write the complete factored form

Question

Write the complete factored form and expanded form of the polynomial with leading coefficient -3 and zeros 4, -2 and 2.

Answer 1

With zeros of 4, -2, and 2, your respective factors will be (x - 4)(x + 2)(x - 2).

Since there is a leading coefficient of -3, the complete factor form is:

-3(x - 4)(x + 2)(x - 2)

To find the expanded form, multiply the factors and combine like terms:

-3(x - 4)(x² + 2x - 2x - 4)

-3(x - 4)(x² - 4)

-3(x³ - 4x² - 4x + 16)

-3x³ + 12x² + 12x - 48