If p(x) = 5x^2 - 4x + 3, what is p(x) + p(-x)?
Answer and explanation
Correct answer: 10x^2 + 6
The governing idea is substitution of -x and cancellation of odd-power terms. We have p(-x) = 5(-x)^2 - 4(-x) + 3 = 5x^2 + 4x + 3, because the square term remains positive while the linear term changes sign. Adding the two expressions gives p(x) + p(-x) = (5x^2 - 4x + 3) + (5x^2 + 4x + 3) = 10x^2 + 6. Thus option A is correct. The x terms cancel. Option B incorrectly retains them, option C omits one x^2 contribution, and option D treats the quadratic terms as if they disappeared.
Frequently asked questions
What is the correct answer to this question?
10x^2 + 6
Why is this the correct answer?
The governing idea is substitution of -x and cancellation of odd-power terms. We have p(-x) = 5(-x)^2 - 4(-x) + 3 = 5x^2 + 4x + 3, because the square term remains positive while the linear term changes sign. Adding the two expressions gives p(x) + p(-x) = (5x^2 - 4x + 3) + (5x^2 + 4x + 3) = 10x^2 + 6. Thus option A is correct. The x terms cancel. Option B incorrectly retains them, option C omits one x^2 contribution, and option D treats the quadratic terms as if they disappeared.
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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