Use the Factor Theorem to determine whether g(x) is a factor of p(x) in the following case:-

*p*(*x*) = *x*^{3} − 4*x*^{2} + *x* + 6, *g*(*x*) = *x* − 3

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#### Solution

If *g*(*x*) = *x* − 3 is a factor of the given polynomial *p*(*x*), then *p*(3) must be 0.

*p*(*x*) = *x*^{3} − 4 *x*^{2} + *x* + 6

*p*(3) = (3)^{3} − 4(3)^{2} + 3 + 6

= 27 − 36 + 9

= 0

Hence, *g*(*x*) = *x* − 3 is a factor of the given polynomial.

Concept: Factorising the Quadratic Polynomial (Trinomial) of the type ax2 + bx + c, a ≠ 0.

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