Write the polynomial function, in standard form, that has zeros -1, -2, and 3:

Question

Write the polynomial function, in standard form, that has zeros -1, -2, and 3:

Answer 1

If the zeroes of the function are -2, -1, and 3, then you can write the binomial factors as:

 

(x + 2)

(x + 1)

(x - 3)

 

Now, to write the function in standard form, multiply the binomials:

 

(x + 2)(x + 1)(x - 3)

(x + 2)(x² - 3x + x - 3)

(x + 2)(x² - 2x - 3)

x³ - 2x² - 3x + 2x² - 4x - 6

x³ - 7x - 6

 

The function is x³ - 7x - 6.