Question

HELP ASAP!!

Find the product of (x − 6)^2 and is the product a polynomial.
x^2 − 12x + 36; is a polynomial
x^2 − 12x + 36; may or may not be a polynomial
x^2 − 36; is a polynomial
x^2 − 36; may or may not be a polynomial

Answer 1

Answer: Choice A

x^2-12x+36; is a polynomial

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Step-by-step explanation:

Use the rule that (A-B)^2 = A^2 - 2AB + B^2 to show (x-6)^2 = x^2-12x+36 is an identity. In this case, A = x and B = 6

You could also use the FOIL rule or the distributive property as two alternatives.

The result is a polynomial because it consists of summing or subtracting various monomials. If we had terms that had say exponents of decimal numbers or negative values, then we wouldn't have a polynomial.