Chapter 8.6, Problem 32P

Open-Ended Find two different values that complete each expression so that the trinomial can be factored into the product of two binomials. Factor your trinomials.

$4x^2+\square x+12$

To determine

To determine the value so that trinomial can factored into the product of two binomials.

Answer to Problem 32P

18, 49

Explanation of Solution

Given information :

  

Here let us take the value 49.

Hence the factors becomes,

  $\begin{array}{c}4x^2+49x+12=4x^2+48x+1x+12\\ =4x\left(x+12\right)+\left(x+12\right)\\ =\left(4x+1\right)\left(x+12\right)\end{array}$

Now let us take the value 18.

Now the factors becomes,

  $\begin{array}{c}4x^2+18x+12=4x^2+12x+4x+12\\ =4x\left(x+3\right)+4\left(x+3\right)\\ =\left(4x+4\right)\left(x+3\right)\end{array}$