Chapter 7.6, Problem 17E

To determine

To factor: The trinomial $-3t^2+11t-6$ .

Answer to Problem 17E

  $-3t^2+11t-6$

  $=-(t-3)(3t-2)$

Explanation of Solution

Given information: Trinomial $-3t^2+11t-6$ is given.

Calculation:

Here, $a=-3$ is negative.

So factoring -1 from each term of the trinomial,

  $-3t^2+11t-6=-(3t^2-11t+6)$

Because $b=-11$ is negative and $c=6$ is positive, both factors of $c$ must be negative.

Using a table to organize information about the factors of $a$ and $c$ ,

  $\begin{array}{llll}\begin{array}{c}Factors\\ of3\end{array}\hfill & \begin{array}{c}Factors\\ of6\end{array}\hfill & \begin{array}{c}Possible\\ factorization\end{array}\hfill & \begin{array}{c}Middle\\ term\end{array}\hfill \\ 1,3\hfill & -1,-6\hfill & (t-1)(3t-6)\hfill & -6t-3t=-9t\hfill \\ 1,3\hfill & -6,-1\hfill & (t-6)(3t-1)\hfill & -t-18t=-19t\hfill \\ 1,3\hfill & -2,-3\hfill & (t-2)(3t-3)\hfill & -3t-6t=-9t\hfill \\ 1,3\hfill & -3,-2\hfill & (t-3)(3t-2)\hfill & -2t-9t=-11t\hfill \end{array}$

So, $-(3t^2-11t+6)$

  $=-(t-3)(3t-2)$ .