Question : If $(x–4)(x^2+4x+16)=x^3–p$, then $p$ is equal to:
Option 1: 27
Option 2: 8
Option 3: 64
Option 4: 0
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Answer (1)
19th Jan, 2024
Correct Answer: 64
Solution :
Given: $(x–4)(x^2+4x+16)=x^3–p$
Formula: We know that $a^3–b^3=(a–b)(a^2+ab+b^2)$
Solution:
$x^3–p=(x–4)(x^2+4x+16)$
⇒ $x^3−p=(x^3−4^3)$
⇒ $p = 4^3$
So, $p = 64$.
Hence, the correct answer is 64.
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