Chapter A.3, Problem 144AYU

To determine

To find: The statement of “what do you look for first when factoring a problem, and what do you do next?”

Answer to Problem 144AYU

The reverse distribution method is used to solve the problem.

Explanation of Solution

Given information:

Solve the factoring problem first look to see if it see quadratic trinomial. This is often easier to factor than higher degree polynomials.

First these factors of $c$ that add to be $b$ are $d$ and $e$ ,the factor trinomial would be written as $x^2+bx+c=\left(x+d\right)\left(x+e\right)$ .

If is a higher degree polynomial, first look to see if it is a quadratic trinomial is disguise example a polynomial of the form $x^6+b{x}^3+c$ could be written as quadratic trinomial

  $y^2+by+c$ where $y=x^3$

If the higher degree polynomial with 4 terms,

  $\begin{array}{c}{x}^4-7x^3+x-7=x^3\left(x-7\right)+1\left(x-7\right)\\ =\left(x^3+1\right)\left(x-7\right)\end{array}$

Therefore, this method is sometimes called reverse distribution.