Chapter 8.4, Problem 60HP

To determine

Find the two binomials with a product that is a binomial and also write two binomial with a product that is not a binomial.

Answer to Problem 60HP

The example for first case is $(5+4x)\cdot (3+2x)$ such that $x^2=-1$ , and second case is $(5+4x)\cdot (3+2x)$ .

Explanation of Solution

Given:

It is given in the question that there would be a binomial.

Since for the first case such that the product of the two binomial is a binomial but in this case, it has to put specific condition so as to get the binomial Let’s take example: $(5+4x)\cdot (3+2x)$ such that $x^2=-1$ ,

  $\begin{array}{l}(5+4x)\cdot (3+2x)\\ 15+10x+12x+8x^2\\ 15+22x+8\cdot -1\\ 15+22x-8\\ 7+22x\end{array}$

which is binomial having certain condition.

At last, the product of the two binomial is not a binomial,

  $\begin{array}{l}(5+4x)\cdot (3+2x)\\ 15+10x+12x+8x^2\\ 15+22x+8x^2\end{array}$

which is without condition and it is a trinomial.