### Home > PC > Chapter 9 > Lesson 9.3.2 > Problem 9-116

Show whether or not *x* − 5 is a factor of *x*^{3} + 4*x*^{2} − 11*x* − 30. Homework Help ✎

Set up the generic rectangle with the divisor on the left of the box. Input only the first terms of the dividend.

Since *x* divides into *x*³, *x*² times, write the *x*² on top and multiply *x*² with the −5 and fill in the grid with the product.

Add an expression to −5*x*² in order to get the needed 4*x*². Add it to the right of *x*³.

Dividing *x* into 9*x*² gives 9*x*. Add the 9*x* at the top. Then multiply 9*x* and −5 and fill the answer in the grid.

Add an expression to −45*x* in order to get the needed −11*x*. Add it to the right of 9*x*².

Dividing *x* into 34*x* gives 34. Add the 34 at the top. Then multiply 34 and −5 and fill the answer in the grid.

Add an expression to −170 in order to get the needed −30. Add it to the right of 34*x*. This is the remainder. Add it to the top as a ratio.

Since there is a remainder, *x* − 5 is not a factor!