Provide an appropriate response.Factor the polynomial 5a4 + 34a2 - 7. Explain the method used.
What will be an ideal response?
The polynomial 5a4 + 34a2 - 7 is factored completely as (5a2 - 1)(a2 + 7).
Let u = a2, and substitute this into (5a4 + 34a2 - 7).
5a4 + 34a2 - 7 = 5u2 + 34u - 7
5u2 + 34u - 7 = (5u - 1)(u + 7)
Finally, substitute back u = a2
(5u - 1)(u + 7) = (5a2 - 1)(a2 + 7)
(Explanations will vary.)
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