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If \(p(x)=x^3+3x^2+3x+1\), what is the value of \(p(-2)\)?यदि \(p(x)=x^3+3x^2+3x+1\), तो \(p(-2)\) का मान क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: -1-1
The polynomial matches the identity \(a^3+3a^2b+3ab^2+b^3=(a+b)^3\), so \(p(x)=(x+1)^3\). Hence, \(p(-2)=(-2+1)^3=(-1)^3=-1\). The value 0 would result from incorrectly substituting \(x=-1\). Exam tip: look for the perfect-cube identity before expanding or calculating term by term.दिए गए बहुपद में \(x^3+3x^2+3x+1=(x+1)^3\) की पहचान लागू होती है। इसलिए \(p(-2)=(-2+1)^3=(-1)^3=-1\)। विकल्प 0 तब मिलता यदि \(x=-1\) रखा जाता, इसलिए वह गलत है। परीक्षा-युक्ति: घन बहुपद में \(a^3+3a^2b+3ab^2+b^3=(a+b)^3\) की पहचान अवश्य जाँचें।
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