Question

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

Answer 1

Answer:

$A = 6$.

Step-by-step 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:

$(-3)^3 - (-3)^2 - 10\times (-3) + A$.

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