Question

In the following pair of polynomials, the second polynomial is a factor of the first. Factor completely x^3+3x^2-18x , x-4

Answer 1

Answer:

The required factors are: x, (x + 6) and (x - 3).

Step-by-step explanation:

As per the question,

The given polynomial is:

$x^{3}+3x^{2}-18x$

Now,

BY factorization, we get

$x^{3}+3x^{2}-18x$

$=x(x^{2}+3x-18)$

By splitting the mid-term, that is split 3x like:

3x = 6x - 3x

Therefore,

$x(x^{2}+6x-3x-18)$

Now on further solving by taking common factor out, we get

$=x[x(x+6)-3(x+6)]$

$=x(x+6)(x-3)$

Therefore, the given second polynomial (x - 4), is not a factor of given polynomial $x^{3}+3x^{2}-18x$.

Hence, the given polynomial has three factor x, (x + 6) and (x - 3).