What is the degree of the sum of (p(x)=4x^4-3x^2+2) and (q(x)=-4x^4+5x^3+x-8)?
Answer and explanation
Correct answer: (3)
To find the degree of a sum, first add like terms and then inspect the highest power whose coefficient is not zero. Adding the polynomials gives (4x^4-3x^2+2)+(-4x^4+5x^3+x-8). The x^4 terms cancel because 4x^4-4x^4=0. The remaining polynomial is 5x^3-3x^2+x-6.
The highest power still present is x^3, whose coefficient is 5, not zero. Therefore the degree of the sum is 3, so choice C is correct. A common error is to retain degree 4 merely because both original polynomials had degree 4. Degree can decrease after addition when leading terms cancel, so the resulting expression must always be simplified before its degree is stated.
Frequently asked questions
What is the correct answer to this question?
(3)
Why is this the correct answer?
To find the degree of a sum, first add like terms and then inspect the highest power whose coefficient is not zero. Adding the polynomials gives (4x^4-3x^2+2)+(-4x^4+5x^3+x-8). The x^4 terms cancel because 4x^4-4x^4=0. The remaining polynomial is 5x^3-3x^2+x-6.
The highest power still present is x^3, whose coefficient is 5, not zero. Therefore the degree of the sum is 3, so choice C is correct. A common error is to retain degree 4 merely because both original polynomials had degree 4. Degree can decrease after addition when leading terms cancel, so the resulting expression must always be simplified before its degree is stated.
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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