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Divide the polynomials. Your answer should be a polynomial. (x^(2)-36)/(x-6)=◻

Divide the polynomials. Your answer should be a polynomial.\newlinex2−36x−6=□ \frac{x^{2}-36}{x-6}=\square

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Full solution

Q. Divide the polynomials. Your answer should be a polynomial.\newlinex2−36x−6=□ \frac{x^{2}-36}{x-6}=\square
  1. Recognize the numerator: Recognize the numerator as a difference of squares.\newlineThe numerator x2−36x^2 - 36 can be factored into (x+6)(x−6)(x + 6)(x - 6) because it is a difference of squares where a2−b2=(a+b)(a−b)a^2 - b^2 = (a + b)(a - b).
  2. Write the division as a fraction: Write the division as a fraction and factor the numerator. (x2−36)/(x−6)=[(x+6)(x−6)]/(x−6)(x^2 - 36) / (x - 6) = [(x + 6)(x - 6)] / (x - 6)
  3. Cancel out the common factor: Cancel out the common factor (x−6)(x - 6) from the numerator and the denominator.(x+6)(x−6)(x−6)=x+6\frac{(x + 6)(x - 6)}{(x - 6)} = x + 6
  4. Write down the final answer: Write down the final answer.\newlineThe result of the division is x+6x + 6.

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