Question

A farmhand is building two pig pens of the same width, but different lengths. If x is the common width, in meters, then the cost of building one pen is 34x^2-4x+22 dollars, and the cost of building the other pen is 22x² + 4x + 46.5 dollars. What's the total cost of building those two pens? A polynomial representing the total cost of building those two pens is dollars

Answer 1

To find the total cost of building both pens we need to add the cost of each pen. When adding polynomials we need to add those that have the same literal part. With this in mind let's solve the problem:

$\begin{gathered} \text{pen}1=34x^2-4x+22 \\ \text{pen}2=22x^2+4x+46.5 \\ \text{total cost = pen1+pen2} \\ \text{total cost = 34x}^2-4x+22+22x^2+4x+46.5 \\ \text{total cost = 34x}^2+22x^2-4x+4x+22+46.5=56x^2+68.5 \end{gathered}$

The cost of building both pens can be represented by the polynomial 56x² + 68.5