Chapter SH, Problem 14.8.4EP

To determine

To factor: the given polynomial

Answer to Problem 14.8.4EP

The required result is $\left(x-2\right)\left(x-4\right)$ .

Explanation of Solution

Given: $x^2-6x+8$

Calculation:

Write the trinomial as the product of two binomials.

Product of first terms is $x^2$ .

  $x^2-6x+8=\left(x+?\right)\left(x+?\right)$

Now find the two terms whose product must be $8$ .

Try several factors of $8$ so that sum of the product of outer and inner terms must be $-6x$ .

Try the factors $1,8$ .

  $\begin{array}{l}\left(x+1\right)\left(x+8\right)=x^2+x+8x+8\\ =x^2+9x+8\end{array}$

It is not true.

Try the factor $-2,-4$ .

  $\begin{array}{l}\left(x-2\right)\left(x-4\right)=x^2-2x-4x+8\\ =x^2-6x+8\end{array}$

It is true.

Hence, the result is $\left(x-2\right)\left(x-4\right)$ .

Conclusion:

Hence, the factorization is $\left(x-2\right)\left(x-4\right)$ .