Chapter 1.3, Problem 56PPSE

Solution

To state: An example of an algebraic expression that has a nonnegative value regardless of the value of the variable.

The algebraic expression is $6x^2+8$ .

Given information:

The given statement says to give an example of an algebraic expression that has a nonnegative value regardless of the value of the variable.

Explanation:

Consider an algebraic expression:

  $6x^2+8$ .

To check the algebraic expression, substitute positive, negative values and zero for x in the expression.

Substitute x as 5 (positive value) in the expression $6x^2+8$:

  $6x^2+8=6{\left(5\right)}^2+8$

Simplify the power,

  $6\left(25\right)+8$

Multiply and add,

  $150+8=158$

Now substitute x as -4 (negative value) in the expression $6x^2+8$ :

  $6x^2+8=6{\left(-4\right)}^2+8$

Simplify the power,

  $6\left(16\right)+8$

Multiply and add,

  $96+8=104$

Now substitute x as 0 in the expression $6x^2+8$:

  $6x^2+8=6{\left(0\right)}^2+8$

Simplify the power,

  $6\left(0\right)+8$

Multiply and add,

  $8$

Therefore, it can be seen that for every value of x , the resultant answer is positive.