Find a polynomial function that has the given zeros Show wor

Find a polynomial function that has the given zeros Show work. 4i, -4i, -1 Use Remainder Theorem to find P(c). (You must this method to receive credit.) Show work. P(x) = 3x^2 + x^2 + x - 5, c = 2

Solution

Given that the polynomial has zeros 4i, -4i, -1.

Need to find the polynomial.

Let the polynomial is P(x).

P(x) = (x-(4i))(x-(-4i))(x-(-1))

= (x-4i)(x+4i)(x+1)

= [x² - (4i)²](x+1) ( since (a+b)(a-b) = a² - b² )

= [x² - 16i²](x+1)

= [x² - 16(-1)](x+1) (i² = -1)

= [x² + 16](x+1)

= x²(x+1) + 16(x+1)

= x³ + x² + 16x +16

Therefore, required polynomial P(x) = x³ + x² + 16x +16