SOLUTION: Please help me figure out the following: A countertop will have a hole drilled in it to hold a cylindrical container that will function as a utensil holder. The area of the en

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Please help me figure out the following: A countertop will have a hole drilled in it to hold a cylindrical container that will function as a utensil holder. The area of the en      Log On


   

Question 428394: Please help me figure out the following:
A countertop will have a hole drilled in it to hold a cylindrical container that will function as a utensil holder. The area of the entire countertop is given by 5x squared plus 12x plus 7. The area of the hole is given by x squared plus 2x plus 1. Write an expression for the area in factored form of the countertop that is left after the hole is drilled.
Thanks!
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A countertop will have a hole drilled in it to hold a cylindrical container that will function as a utensil holder. The area of the entire countertop is given by 5x squared plus 12x plus 7. The area of the hole is given by x squared plus 2x plus 1. Write an expression for the area in factored form of the countertop that is left after the hole is drilled.
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Remaining area = (5x^2+12x+7)-(x^2+2x+1) = 4x^2+10x+6
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Factor:
4x^2+10x+6
= 2(2x^2+5x+3)
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= 2(2x^2+4x+x+2)
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= 2(2x(x+2)+(x+2))
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= 2(x+2)(2x+1)
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Cheers,
Stan H.
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