If (p(x)=x+4) and (q(x)=x-4), what type of polynomial is (p(x)q(x))?
Answer and explanation
Correct answer: Quadratic polynomial
\(p(x)q(x)=(x+4)(x-4)=x^2-16\), using the identity \((a+b)(a-b)=a^2-b^2\). The highest power of \(x\) is 2, so its degree is 2 and it is a quadratic polynomial. A linear polynomial has degree 1, so option A is not correct. Exam tip: Before multiplying, look for conjugate factors to apply the difference-of-squares identity.
Frequently asked questions
What is the correct answer to this question?
Quadratic polynomial
Why is this the correct answer?
\(p(x)q(x)=(x+4)(x-4)=x^2-16\), using the identity \((a+b)(a-b)=a^2-b^2\). The highest power of \(x\) is 2, so its degree is 2 and it is a quadratic polynomial. A linear polynomial has degree 1, so option A is not correct. Exam tip: Before multiplying, look for conjugate factors to apply the difference-of-squares identity.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Introduction to Polynomials. Topic: Linear polynomials.
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