Question

If x+3 is a factor of x^3-x^2-10x+A. What is the value of A?

Answer 1

`A = 6`.

Explanation:

Let
`a` denote a constant (a number, rather than a variable like
`x`.)

Let
`f(x)` denote an expression about
`x` (for example,

By the factor theorem, if
`(x - a)` is a factor of
`f(x)`, then
`f(a) = 0`. In other words, if all mentions of
`x` in the expression
`f(x)\!` are replaced with
`a`, then the expression should evaluate to zero.

`(x + 3)` is equivalent to
`(x - (-3))`. That is:
`a = -3`.

Replace all mentions of
`x` in
`x^3 - x^2 - 10\, x + A` by
`(-3)` to get:

`(-3)^3 - (-3)^2 - 10* (-3) + A`.

That should evaluate to zero. Therefore:
`-27 - 9 + 30 + A = 0`. Solve for
`A` to get
`A = 6`.