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The area (in square inches) of a rectangle is given by the polynomial function A(y)=y²+12y+35
. If the width of the rectangle is (y+5)
inches, what is the length of the

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Answer:

Length =  (y + 7)

Step-by-step explanation:

Area of the rectangle:
A = y² + 12y + 35

We can factor this polynomial as follows

  • Find two numbers a and b such that ab = 35 and a + b = 12
  • The only two values for a, b are 5 and 7
  • Therefore
    y² + 12y + 35 =(y + 7) (y + 5)

The area of a rectangle is given by LW where L = length and W = width

So, LW = (y + 7) (y + 5)

Given W = (y + 5), L must be (y + 7)

Answer: Length of rectangle = (y + 7)

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