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If the expressions (px3 + 3x2 – 3) and (2x3 – 5x + p) when divided by (x – 4) leave the same remainder, then what is the value of p ?

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Let f(x) = px3 + 3x2 – 3 

g(x) = 2x3 – 5x + p 

When divisible by x – 4, the remainders for the given expressions are f(4) and g(4) respectively. 

f(4) = p(4)3 + 3(4)2 – 3 = 64p + 48 – 3 = 64p + 45 

g(4) = 2(4)3 – 5(4) + p = 128 – 20 + p = 108 + p. 

Given, f(4) = g(4) ⇒ 64p + 45 = 108 + p ⇒ 63 p = 63 ⇒ p = 1.

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