integral polynomials

[marsh rampart]

Need help finding the integral polynomial whose roots are 3, 2/5 and -1/2

(I have no idea how to do this LIKE 0, like is this even possible)

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[restive tiger]

Given a polynomial f with a root of x = c, (x-c) is a factor of f

1. What are the three roots of f
2. What are the three factors of f
3. What is the product of those factors (aka f)

[marsh rampart]

How do I get the factors

Like whats c

[restive tiger]

Notice how 3, or x = 3, is a root of the polynomial
This means that (x-3) is a factor of the polynomial

[marsh rampart]

Oooh ok so (x-2/5) and (x+1/2)

How do I get the product of the factors

[restive tiger]

Multiply them out

[marsh rampart]

Where do I multiply them

[restive tiger]

Like multiply (x-3)(x-2/5)(x+1/2) and the result is your polynomial

[marsh rampart]

I got x^3+-29/10x^2+-1/2x+3/5

Is that it

[winter aspen]

dont forget the constant too

when k is R-{0}
kP(x) doesn't change the answer

[marsh rampart]

Wait what's the constanr

[marsh rampart]

I thought this was final

[winter aspen]

just multiply that by k and say that k ∈ R-{0} should be good

[marsh rampart]

Oh I multiply this by 3/5

just got x^3+-29x^2/10-x/2+9/25