Question

Write a polynomial in standard form with zeros 1, 2, and −5.

a. x^3 – 2x^2 + 13x – 10 = 0
b. x^3 – 4x^2 + 17x + 10 = 0
c. x^3 + 2x^2 – 13x + 10 = 0
d. x^3 + 6x^2 – 3x + 10 = 0

Answer 1

Explanation:

First thing you have to do is write those zeros into factors. If

x = 1, then its factor is (x - 1). If

x = 2, then its factor is (x - 2). If

x = -5, then its factor is (x + 5).

Now we FOIL them all together, starting with the first 2:

(x - 1)(x - 2) =
`x^2--2x-1x+2`

Combine like terms to get

`x^2-3x+2`

Now FOIL that with the last factor to get

`x^3-3x^2+2x+5x^2-15x+10`

Combine like terms to get

`x^3+2x^2-13x+10=0`, which is choice C