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ASHA 777 [7]
3 years ago
6

a rectangular box is 24 in. long, 12 in wide, and 18 in high. If each dimension is increased by x in .. write a polynomial funct

ion in standard form modeling the volume of the box
Mathematics
1 answer:
ziro4ka [17]3 years ago
8 0

Answer:

<h2>V = x³ + 54x² + 936x + 5,184</h2>

Step-by-step explanation:

<h3 /><h3>If we add a value of 'x' to each side of the box, the new dimensions can be represented as</h3><h3>x + 24</h3><h3>x + 12 and </h3><h3>x + 18</h3><h3 /><h3>To find the volume of the new box, multiply all of the dimensions together</h3><h3 /><h3>V = (x + 24)(x + 12)(x + 18)    </h3><h3> Foil the first and second binomial....</h3><h3 /><h3>V = (x² + 36x + 288)(x + 18)</h3><h3>  Now multiply the two polynomials together...</h3><h3 /><h3>V = x²(x) + 36x(x) + 288x + x²(18) + 36x(18) + 288(18)</h3><h3 /><h3>V = x³ + 36x² + 288x + 18x² + 648x + 5,184</h3><h3 /><h3>which simplifies to</h3><h3 /><h3>V = x³ + 54x² + 936x + 5,184     where x represents the increase in inches</h3>
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