Chapter SH, Problem 14.8.7EP

To determine

To factor: the given polynomial

Answer to Problem 14.8.7EP

The required result is $\left(x-3\right)\left(x-3\right)$ .

Explanation of Solution

Given: $x^2-6x+9$

Calculation:

Write the trinomial as the product of two binomials.

Product of first terms is $x^2$ .

  $x^2-6x+9=\left(x+?\right)\left(x+?\right)$

Now find the two terms whose product must be $+9$ .

Try several factors of $+9$ so that sum of the product of outer and inner terms must be $-6x$ .

Try the factors $1,9$ .

  $\begin{array}{l}\left(x+1\right)\left(x+9\right)=x^2+x+9x+9\\ =x^2+10x+9\end{array}$

It is not true.

Try the factor $-3,-3$ .

  $\begin{array}{l}\left(x-3\right)\left(x-3\right)=x^2-3x-3x+9\\ =x^2-6x+9\end{array}$

It is true.

Hence, the result is $\left(x-3\right)\left(x-3\right)$ .

Conclusion:

Hence, the factorization is $\left(x-3\right)\left(x-3\right)$ .