For (p(x)=2x^3+x^2-5x+2), what is the difference (p(2)-p(-1))?
Answer and explanation
Correct answer: (6)
To find the difference \\(p(2)-p(-1)\\), evaluate the polynomial at both inputs separately and then subtract the second result from the first. Careful handling of the negative value is important, especially for the cubic term. The two values are 12 and 6, so their difference is 6. Hence option D is correct.
For x=2, \\(p(2)=2(2)^3+(2)^2-5(2)+2=16+4-10+2=12\\). For x=-1, \\(p(-1)=2(-1)^3+(-1)^2-5(-1)+2=-2+1+5+2=6\\). Therefore \\(p(2)-p(-1)=12-6=6\\). The signs in \\((-1)^3\\) and \\(-5(-1)\\) must be handled carefully; confusing them can lead to another option.
Frequently asked questions
What is the correct answer to this question?
(6)
Why is this the correct answer?
To find the difference \\(p(2)-p(-1)\\), evaluate the polynomial at both inputs separately and then subtract the second result from the first. Careful handling of the negative value is important, especially for the cubic term. The two values are 12 and 6, so their difference is 6. Hence option D is correct.
For x=2, \\(p(2)=2(2)^3+(2)^2-5(2)+2=16+4-10+2=12\\). For x=-1, \\(p(-1)=2(-1)^3+(-1)^2-5(-1)+2=-2+1+5+2=6\\). Therefore \\(p(2)-p(-1)=12-6=6\\). The signs in \\((-1)^3\\) and \\(-5(-1)\\) must be handled carefully; confusing them can lead to another option.
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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