For the polynomial P(x)=2x^3-5x^2+x-7, what is the value of P(-1)?
Answer and explanation
Correct answer: -15
The governing concept is evaluation of a polynomial by substitution. Replace every occurrence of x with -1, keeping brackets so that the signs and powers are handled correctly: P(-1)=2(-1)^3-5(-1)^2+(-1)-7. Since (-1)^3=-1 and (-1)^2=1, this becomes 2(-1)-5(1)-1-7=-2-5-1-7=-15. Thus option A is correct. Option B usually results from an arithmetic or sign error, option C reverses the final sign, and option D does not represent the value of the complete polynomial.
Frequently asked questions
What is the correct answer to this question?
-15
Why is this the correct answer?
The governing concept is evaluation of a polynomial by substitution. Replace every occurrence of x with -1, keeping brackets so that the signs and powers are handled correctly: P(-1)=2(-1)^3-5(-1)^2+(-1)-7. Since (-1)^3=-1 and (-1)^2=1, this becomes 2(-1)-5(1)-1-7=-2-5-1-7=-15. Thus option A is correct. Option B usually results from an arithmetic or sign error, option C reverses the final sign, and option D does not represent the value of the complete polynomial.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Operations on real numbers and the laws of exponents.
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