Question

How do you use synthetic division to find if x+1 is a factor for `f(x)=2x^3+5x^2-x-4`?

Answer 1

Using synthetic division as shown below would result in a zero remainder.

Explanation:

If: `x+1` is a factor then: `x=-1` is a root/zero of the polynomial:

`f(x)=2x^3+5x^2-x-4`

hence synthetic division should produce a zero remainder.

`.......... 2 ........ 5 ...... -1 ...-4`
`-1 | darr...-2......-3.........4`
`.......... 2.........3...... -4........0=>` Remainder

Quotient `=2x^2+3x-4`