By what factor should the velocity of a body be increased so that its kinetic energy is increased by a factor of nine.
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"by a factor of " is used commonly to mean the same as "multiplied by" or "divided by." If x is INCREASED by a factor of 4, it becomes 4x. If x is DECREASED by a factor of 4, it becomes x/4. The key word is the direction of change i.e. (increased / decreased) by a factor of.
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