Sharon is paving a rectangular concrete driveway on the side of her house. The area of the driveway is 5x^2 + 43x - 18, and the
length of the driveway is x + 9. Additionally, Sharon plans to install a carport over a small portion of the driveway. The volume that the carport can enclose is 48x^3 + 68x^2 - 8x - 3, and the area of driveway beneath the carport is 8x^2 + 10x - 3.
Determine the width of the entire driveway and height of the carport in terms of x. Replace the values of m and b to complete the expression that represents the width of the entire driveway on the first line, and then replace the values of m and b to complete the expression that represents the height of the carport on the second line.
You have to type the answer in mx+b
im just trying to graduate....
The width of the driveway is 5x-2. The height of the carport is 6x+1.
We complete polynomial long division for both of these.
For the driveway: Dividing 5x²+43x-18 by x+9, we first see how many times x will go into 5x². It goes in 5x times; we write this in the division problem above 43x. Multiplying back through, 5x(x+9) = 5x²+45x. This goes below 5x²+43x. We now subtract: 5x²+43x-(5x²+45x)= -2x; this goes below the 45x we wrote earlier. Bring down the -18. Now we see how many times x goes into -2x; it goes -2 times. This goes beside our 5x in our answer at the top. Multiplying back through, -2(x+9) = -2x-18. This goes below our -2x-18 we had, and gives us an answer of 5x-2 with a remainder of 0.
For the carport: To divide 48x³+68x²-8x-3 by 8x²+10x-3, we see how many times 8x² will go into 48x³. It will go 6x times; write this above -8x. Multiplying back through, 6x(8x²+10x-3) = 48x³+60x²-18; write this below 48x³+68x²-8x. Now subtract: 48x³+68x²-8x-(48x³+60x²-18) = 8x²+10x; this goes below our 48x³+60x²-18. Bring down the -3. Now we want to see how many times 8x² will go into 8x². It goes 1 time; write this beside our 6x at the top. Multiplying back through, 1(8x²+10x-3) = 8x²+10x-3; write this below the 8x²+10x-3 we have already down. When we subtract these, we get a remainder of 0, with our answer up top as 6x+1.
