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\left(t-7\right)\left(-t^{2}-t-7\right)
By Rational Root Theorem, all rational roots of a polynomial are in the form \frac{p}{q}, where p divides the constant term 49 and q divides the leading coefficient -1. One such root is 7. Factor the polynomial by dividing it by t-7. Polynomial -t^{2}-t-7 is not factored since it does not have any rational roots.