If p(x)=4x^2-3x+2, what is p(x)+p(-x)?
Answer and explanation
Correct answer: 8x^2+4
The governing idea is substitution followed by combining like terms. Replacing x by -x gives p(-x)=4(-x)^2-3(-x)+2=4x^2+3x+2, because an even power keeps its sign while the linear term changes sign. Therefore, p(x)+p(-x)=(4x^2-3x+2)+(4x^2+3x+2)=8x^2+4. The terms -3x and +3x cancel exactly. Option B incorrectly retains the original linear term, option C omits one quadratic contribution, and option D has the wrong degree and coefficients. Thus option A is the only correct result.
Frequently asked questions
What is the correct answer to this question?
8x^2+4
Why is this the correct answer?
The governing idea is substitution followed by combining like terms. Replacing x by -x gives p(-x)=4(-x)^2-3(-x)+2=4x^2+3x+2, because an even power keeps its sign while the linear term changes sign. Therefore, p(x)+p(-x)=(4x^2-3x+2)+(4x^2+3x+2)=8x^2+4. The terms -3x and +3x cancel exactly. Option B incorrectly retains the original linear term, option C omits one quadratic contribution, and option D has the wrong degree and coefficients. Thus option A is the only correct 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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