Question

What is a polynomial function in standard form with zeroes 1, 2, -2, and -3? (1 point)

Ox4 + 2x3 + 7x2 - 8x + 12
Ox4 + 2x3 - 7x2 - 8x + 12
0x4 + 2x - 7x2 + 8x + 12
x4 + 2x3 + 7x2 + 8x + 12

Answer 1

To find the polynomial function in standard form with the given zeroes, we can use the zero-product property to determine the factors and multiply them together.

Step-by-step explanation:

A polynomial function in standard form with zeroes 1, 2, -2, and -3 can be determined by using the zero-product property. This property states that if a polynomial has a zero at a certain value, then it must have a factor of (x - zero). So, to find the polynomial function, we can use the factors (x - 1), (x - 2), (x + 2), and (x + 3) and multiply them together.

(x - 1)(x - 2)(x + 2)(x + 3) = x4 + 2x3 + 7x2 - 8x + 12

Therefore, the polynomial function in standard form with zeroes 1, 2, -2, and -3 is Ox4 + 2x3 + 7x2 - 8x + 12.

Answer 2

f(x) =
`x^(4)` + 2x³ - 7x² - 8x + 12

Step-by-step explanation:

Given the zeros of a polynomial , say x = a, x = b

Then the factors are (x - a), (x - b)

and the polynomial is the product of the factors

Given zeros are x = 1, x = 2, x = - 2, x = - 3 then the factors are

(x - 1), (x - 2), (x + 2), (x + 3), and the polynomial is

f(x) = (x - 1)(x - 2)(x + 2)(x + 3) ← expand pairs of factors using FOIL

= (x² - 3x + 2)(x² + 5x + 6) ← distribute

=
`x^(4)` + 5x³ + 6x² - 3x³ - 15x² - 18x + 2x² + 10x + 12 ← collect like terms

=
`x^(4)` + 2x³ - 7x² - 8x + 12