In the expression , p is a constant. This expression is equivalent to the expression . What is the value

Question

In the expression , p is a constant. This expression is equivalent to the expression . What is the value of p ?

Accepted Answer

Choice B is correct. Using the distributive property, the first given expression can be rewritten as 6 x 2 + 3 px + 24 - 16 px - 64 x + 24, and then rewritten as 6 x 2 + (3 p - 16 p - 64) x + 24. Since the expression 6 x 2 + (3 p - 16 p - 64) x + 24 is equivalent to 6 x 2 - 155 x + 24, the coefficients of the x terms from each expression are equivalent to each other; thus 3 p - 16 p - 64 = -155. Combining like terms gives -13 p - 64 = -155. Adding 64 to both sides of the equation gives -13 p = -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 6x 2 - 25 x + 24. Choice C is incorrect. If p = 13, then the first expression would be equivalent to 6 x 2 - 233 x + 24. Choice D is incorrect. If p = 155, then the first expression would be equivalent to 6 x 2 - 2,079 x + 24.

Question in-the