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the tools blog

help plz cant find the possible racional zero, complete factorization and zero of P.. P(x)= 2x^4-7x^3+x^2+7x-3?

Note that x = 1 is a root of P(x), since P(1) = 0.

By long/synthetic division, we get
P(x) = (x - 1)(2x^3 - 5x^2 - 4x + 3).

Next, x = -1 is a root of 2x^3 - 5x^2 - 4x + 3.
==> P(x) = (x - 1) * (x + 1)(2x^2 - 7x + 3).

Finally, 2x^2 - 7x + 3 = (2x - 1)(x - 3).

Thus, the roots are 1, -1, 1/2, and 3.

I hope this helps!

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