If p(x)=x²−4x+1, what is p(x)−p(1)?
Answer and explanation
Correct answer: x²−4x+3
First calculate the fixed value p(1): p(1)=1²−4(1)+1=1−4+1=−2. Now subtract this value from the general expression: p(x)−p(1)=(x²−4x+1)−(−2)=x²−4x+1+2=x²−4x+3. Therefore option A is correct. The negative sign before p(1) is important: subtracting −2 is the same as adding 2. Option C is merely the original polynomial and ignores the subtraction. Option B would result from subtracting 2 rather than subtracting −2, and option D changes the sign of the linear term without any algebraic basis. The original option list and key were inconsistent; option A has been corrected to the actual result.
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What is the correct answer to this question?
x²−4x+3
Why is this the correct answer?
First calculate the fixed value p(1): p(1)=1²−4(1)+1=1−4+1=−2. Now subtract this value from the general expression: p(x)−p(1)=(x²−4x+1)−(−2)=x²−4x+1+2=x²−4x+3. Therefore option A is correct. The negative sign before p(1) is important: subtracting −2 is the same as adding 2. Option C is merely the original polynomial and ignores the subtraction. Option B would result from subtracting 2 rather than subtracting −2, and option D changes the sign of the linear term without any algebraic basis. The original option list and key were inconsistent; option A has been corrected to the actual result.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Polynomials in one variable.
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