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Linear Polynomial

A linear polynomial is a polynomial of degree one, meaning the highest power of its variable is exactly one. It represents a straight line when plotted on a Cartesian coordinate graph and has exactly one zero or root.

Key Concepts

The standard form of a linear polynomial in one variable x is ax + b, where a and b are real numbers and a is not equal to zero.
The graph of a linear polynomial y = ax + b is always a straight line that intersects the x-axis at exactly one point.
The x-coordinate of the point where the graph intersects the x-axis is the zero of the linear polynomial.

Formula & Equation

P(x) = ax + b

x is the variable, a is the coefficient of x (where a is not equal to 0), and b is the constant term. The zero of the polynomial is given by x = -b/a.

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Common Misconceptions

Myth: A polynomial like P(x) = 5 is a linear polynomial because it has no exponents written.
Fact: P(x) = 5 is a constant polynomial with a degree of zero. A linear polynomial must have a variable with a degree of exactly one, such as P(x) = 5x.

Real World Applications

Calculating the total cost of a taxi ride where there is a fixed base fare plus a constant rate per kilometer traveled.
Converting temperatures from Celsius to Fahrenheit using the linear relationship F = 1.8C + 32.

Frequently Asked Questions

How many zeroes does a linear polynomial have?
A linear polynomial has exactly one zero, which is the point where its graph intersects the x-axis.
What is the general form of a linear polynomial?
The general form is ax + b, where a and b are real numbers and a cannot be zero.

Keep Learning

Degree of a PolynomialZero of a PolynomialGraphical Representation