Determine whether each binomial is a factor of x^3+4x^2+x-6 x+1 x+2 x+3 x-3?

x³ + 4x² + x - 6

you can apply the remainder theorem to discover if each binomial is a factor of the polynomial...

(x - a) is a factor of P(x) if f(a) = 0

for (x + 1), evaluate f(- 1)...

f(- 1) = - 1 + 4 - 1 - 6 = - 4

therefore, (x + 1) is not a factor...

can you do the others ? Why not ? You can try !!

[x³ + 4x² + x - 6 = (x - 1)(x + 2)(x + 3) ]

We can easily see that 1 is a root of the binomial. According to Bezout's theorem, the binomial will have a factor (x-1). Divide it for x-1 we get x^2 + 5x + 6. Now, let's factorize it: x^2 + 5x + 6 = x^2 + 2x + 3x + 6 = (x+2)(x+3). So the the binomial is now factorized into (x-1)(x+2)(x+3)

All the rest is for u :)

p.s: since English is not my mother tongue, so I hope u don't mind if I make some grammatical mistakes :P