Question

factor completely. write your answer with positive exponents.

\\q^{-2} - 4q^{-3} + 3q^{-4} = \\

Explanation:

Factor out the lowest power

Using the Negative Exponent Factoring knowledge point

$$ q^{-2} - 4q^{-3} + 3q^{-4} = q^{-4}(q^2 - 4q + 3) $$

Factor the quadratic trinomial

Using the Factoring Polynomials knowledge point

$$ q^2 - 4q + 3 = (q - 3)(q - 1) $$

Rewrite with positive exponents

Using the Negative Exponent Factoring knowledge point

$$ q^{-4}(q - 3)(q - 1) = \frac{(q - 3)(q - 1)}{q^4} $$

Answer:

Factor completely. Write your answer with positive exponents.

\(q^{-2} - 4q^{-3} + 3q^{-4} =\) <blank>\(\frac{(q - 3)(q - 1)}{q^4}\)</blank>