A linear polynomial is a polynomial where the highest power of the variable is 1. Essentially, it's a polynomial of degree 1.
Here's a more detailed breakdown:
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Polynomial Definition: A polynomial is an expression consisting of variables and coefficients, involving only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.
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Degree of a Polynomial: The degree of a polynomial is the highest power of the variable in the polynomial.
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Linear Polynomial Characteristics:
- The general form of a linear polynomial in one variable (x) is:
ax + b, where 'a' and 'b' are constants, and 'a' is not equal to 0. - The variable 'x' has an exponent of 1 (which is usually not explicitly written).
- When graphed on a coordinate plane, a linear polynomial represents a straight line.
- The general form of a linear polynomial in one variable (x) is:
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Examples:
2x + 5(a = 2, b = 5)x - 3(a = 1, b = -3)-4x(a = -4, b = 0)y + 7(a = 1, b = 7 - Note: 'y' is the variable here, not 'x')
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Non-Examples (Not Linear Polynomials):
x^2 + 3x + 1(Degree 2 - Quadratic)x^3 - 2(Degree 3 - Cubic)√x + 4(Square root is not a polynomial term)1/x + 2(Negative exponent is not allowed in a polynomial)
In summary, a linear polynomial is a simple algebraic expression where the highest power of the variable is one, forming a straight line when graphed.
