Chapter 14, Problem 32PT

To determine

To calculate: The whether the polynomial $x^3+5x^2+6x$ can be factored or not.

Answer to Problem 32PT

The factors of the polynomial expression $x^3+5x^2+6x$ are $x,\left(x+2\right)\text{and}\left(x+3\right)$ .

Explanation of Solution

Given Information:

The polynomial expression is $x^3+5x^2+6x$ .

Calculation:

The given polynomial expression is $x^3+5x^2+6x$ .

Now, find the factors of the polynomial $x^3+5x^2+6x$ .

  $\begin{array}{c}{x}^3+5x^2+6x=x\left(x^2+5x+6\right)\\ =x\left(x^2+2x+3x+6\right)\\ =x\left[x\left(x+2\right)+3\left(x+2\right)\right]\\ =x\left(x+2\right)\left(x+3\right)\end{array}$

Hence, therequired factors of the polynomial expression $x^3+5x^2+6x$ are $x,\left(x+2\right)\text{and}\left(x+3\right)$ .