Question

What polynomial has roots of -4, 2, and 5 ?

Answer 1

(x+4) (x-2) (x-5)

Answer 2

can you explain how you found it

Answer 3

Also, I think my teacher wants it in an equation

Answer 4

if x = -4 then x + 4 = 0
x = 2, then x - 2 = 0
x = 5, then x - 5 = 0

(x+4) (x-2) (x-5)

you have foil them to get the polynomial

Answer 5

ok thanks

Answer 6

I got x^3 - 3x^2 -18x + 40

Answer 7

WM: sourwing is absolutely right. You'll need to multiply out (x+4)(x-2)(x-5) to obtain the polynomial. Write it as f(x) = x^3 + ? + ? + ? (four terms).

Answer 8

Now you could check whether that is correct using synthetic division, if you know synth. div.: Start with x =2:

2 | 1 -3 -18 +40
2
------------------------
1

Answer 9

Or you could do your multiplication in a different order and see whether you obtain the same poloynomial.

Answer 10

ok thanks for your help

Answer 11

You're welcome! But are you going to check your answer?