Linear Polynomial in One Variable
A linear polynomial in one variable is a polynomial of degree 1, usually written as ax + b, where a and b are constants and a is not equal to 0.
Practice This ConceptMain explanation
Teacher explanation
In ax + b, a is the coefficient of x and b is the constant term. The zero of the polynomial is the value of x that makes ax + b equal to 0. This is found by solving ax + b = 0.
Example
For p(x) = 2x - 6, the coefficient of x is 2, the constant term is -6, and the zero is x = 3 because 2(3) - 6 = 0.
Simple analogy
Zero means output becomes zero.
Common confusion
Students often ignore the sign of the constant term. In 4x - 12, the constant is -12, not 12.
Exam tip
When finding the zero, write p(x) = 0 first and then solve step by step. Always verify by substitution.
Study the linear polynomial in one variable diagram carefully
Use the labelled diagram to keep linear polynomial in one variable clear in short answers and revision.
What this diagram makes clear
This diagram keeps the labels and direction of linear polynomial in one variable in the right order.
Where this helps in exams
Use this for labelled diagram work and short exam answers on linear polynomial in one variable.
Revision cue
Revise linear polynomial in one variable through the labels before writing the answer.
Answer writing and exam use
1-mark use
Write the exact meaning of linear polynomial in one variable in one clean line.
2-mark use
Define linear polynomial in one variable and add one example or condition.
3-mark use
Explain linear polynomial in one variable, show the method or example, and mention the common mistake.
Practice this concept with focused MCQs
Open the concept quiz intro first, review the test details, and then start a focused MCQ set from this concept only. Instant score and answer review are live now.
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