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In this Class 9 Mathematics topic from “Introduction to Polynomials,” students learn how to recognize and work with linear polynomials, whose degree is one and which are commonly written as ax + b, where a is non-zero. They identify the variable, coefficient, constant term, and degree, distinguish linear polynomials from other types, evaluate them for given values, and understand how to find their zero. These ideas build a foundation for simplifying expressions and studying polynomial relationships.
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Medium · Level 34 · linear polynomial,coefficient evaluation,simultaneous equations,linear function,Introduction to Polynomials,Class 9 MCQ,Linear polynomials,MathematicsView options
If p(x) = mx + n, p(−3) = 4, and p(2) = 29, what is m + n?
Correct answer: B
Use the definition p(x)=mx+n and substitute the two given input-output pairs. From p(−3)=4, we obtain −3m+n=4. From p(2)=29, we obtain 2m+n=29. Subtracting the first equation from the second eliminates n: (2m+n)−(−3m+n)=29−4, so 5m=25 and m=5. Substitute m=5 into −3m+n=4: −15+n=4, hence n=19. Therefore m+n=5+19=24, so option B is correct. The other choices do not satisfy both original conditions simultaneously; for instance, the value 29 is one given output, not the requested sum of the coefficients.
Given \(p(x)=16x-11\), \(p(x+2)=16(x+2)-11=16x+21\) and \(p(x-3)=16(x-3)-11=16x-59\). Therefore, \(p(x+2)+p(x-3)=(16x+21)+(16x-59)=32x-38\). Option A results from an incorrect addition of the constant terms. Exam tip: always keep \(x-3\) in brackets while substituting it into a polynomial.
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