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Make up two polynomials that factor into a perfect square. Use x as your variable.
Then do this:
A. Add the polynomials
B. Subtract the polynomials
C. Multiply the polynomials.
D. Evaluate the two polynomials when x = 1/7.
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This is a nice exercise that shows how factoring patterns behave in various operations. Try (x+2)^2 and (x−3)^2. You'll see that the symmetry in their construction simplifies the outcomes whether you add, subtract, or multiply them. Additionally, evaluating at x=1/7 demonstrates how small values affect polynomial outputs, serving as a useful reminder of the connection between algebra and real numbers.
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