precalc question

Question

Form a polynomial whose zeros and degree are given.

Zeros: -4,4,3; degree 3. Type a polynomial with integer coefficients and a leading coefficient of 1 in the box below.

Answer 1

First, convert the zeroes into factors of your polynomial:

1. -4 -> (x + 4) [because -4 + 4 = 0]
2. 4 -> (x - 4) [because 4 - 4 = 0]
3. 3 -> (x - 3) [because 3 - 3 = 0]

So our polynomial is: (x + 4)(x - 4)(x - 3)

If we multiply the first two terms using FOIL (First Outside Inside Last), we get:

1. (x + 4)(x - 4) = x² - 4x + 4x - 16 = x² - 16

So our polynomial is now: (x² - 16)(x - 3)

Multiplying the remaining two terms of our polynomial, we get:

1. (x² - 16)(x - 3) = x³ - 3x² - 16x + 48

x³ - 3x² - 16x + 48 is a polynomial of degree 3 (highest power of x) and our answer.