Question 428394
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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