show that (x+4),(x-3) and (x-7) are factors of x^3-6x^2-19x+84.
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Step-by-step explanation:
show that (x+4),(x-3) and (x-7) are factors of x^3-6x^2-19x+84.
x
3
−6x
2
−19x+84
=x
3
+4x
2
−10x
2
−40x+21x+84
=x
2
(x+4)−10(x+4)+21(x+4)
=(x+4)(x
2
−10+21)
=(x+4)(x
2
−7x−3x+21)
=(x+4)[x(x−7)−3(x−7)]
=(x+4))(x−3)(x−7)
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