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If \(f(x)=x^2-1\) and \(g(x)=x-1\), what is the factorized form of \((f-g)(x)\)?यदि \(f(x)=x^2-1\) और \(g(x)=x-1\) हों, तो \((f-g)(x)\) का गुणनखंडित रूप क्या होगा?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(x(x-1)\)\(x(x-1)\)
\((f-g)(x)=f(x)-g(x)=(x^2-1)-(x-1)=x^2-1-x+1=x^2-x=x(x-1)\), so option A is correct. Option B results from mishandling the signs in the subtraction. Exam tip: when subtracting a polynomial, change the sign of every term in the polynomial being subtracted before simplifying.\((f-g)(x)=f(x)-g(x)=(x^2-1)-(x-1)=x^2-1-x+1=x^2-x=x(x-1)\)। इसलिए सही उत्तर A है। विकल्प B में \(-1\) और \(+1\) के संकेतों का गलत प्रयोग हुआ है। परीक्षा-युक्ति: दो बहुपदों का घटाव करते समय दूसरे पूरे बहुपद के प्रत्येक पद का चिह्न बदलें।
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