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Factor Theorem

If 2 x +1 is ...

Question

If 2x + 1 is one factor of the polynomial 2x^2 - x - 1, then find the other factor.

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Solution

2x^2 - x - 1

= 2x^2 - 2x + x - 1

= 2x(x-1) + 1(x-1)

(2x + 1)(x-1)

so (x-1) is the other factor of the polynomial

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