sat-dog

Choice B is correct. Using the distributive property, the first given expression can be rewritten as 6x² + 3px + 24 – 16px – 64x + 24, and then rewritten as 6x² + (3p – 16p – 64)x + 24. Since the expression 6x² + (3p – 16p – 64)x + 24 is equivalent to 6x² – 155x + 24, the coefficients of the x terms from each expression are equivalent to each other; thus 3p – 16p – 64 = –155. Combining like terms gives –13p  – 64 = –155. Adding 64 to both sides of the equation gives –13p = –71. Dividing both sides of the equation by –13 yields p = 7.

Choice A is incorrect. If p = –3, then the first expression would be equivalent to 6x² – 25x + 24. Choice C is incorrect. If p = 13, then the first expression would be equivalent to 6x² – 233x + 24. Choice D is incorrect. If p = 155, then the first expression would be equivalent to 6x² – 2,079x + 24.