Baljit builds a square frame that is 1 inch wider than the width of a square frame from the store. He writes the area enclosed by his frame with the polynomial #4x^2+4x+1#.?

Question

a. Factor the polynomial that Baljit wrote. Explain how the factorization yields an expression for the width of the frame Baljit builds.
B. What is a variable expression for the area enclosed by the frame from the store. Explain how you know.

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Answer 1 · 2018-07-22T21:01:50

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The given polynomial can be factorized as follows

A)

#4x^2+4x+1#

#=4x^2+2x+2x+1#

#=2x(2x+1)+(2x+1)#

#=(2x+1)(2x+1)#

#=(2x+1)^2#

The area of square frame built by Baljit is #(2x+1)^2=\text{(side)}^2#

Hence, the width or side of square frame is #2x+1#

B) Since square frame built by Baljit is #1# inch wider than the square frame from store

hence the side of square frame from store will be #2x+1-1=2x#

Now, the area enclosed by the square frame from store

#\text{(side)}^2#

#=(2x)^2#

#=4x^2#