Polynomials

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A polynomial is an algebraic expression consisting of variables and coefficients, involving only addition, subtraction, multiplication, and non-negative integer exponents. The degree of a polynomial i…

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The expressions 1/x-1, √x + 2, and 1/x² + 2x + 3 are NOT polynomials because they contain negative exponents (1/x = x⁻¹) or fractional exponents (√x = x^(1/2)). Only 2x² - 3x + 1 is a polynomial as it…

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A linear polynomial is a polynomial of degree 1. General form: ax + b, where a ≠ 0. Examples: 2x - 3, √3x + 5, y + √2. Note that expressions like 2x + 5 - x² are not linear polynomials because the hig…

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A quadratic polynomial is a polynomial of degree 2. General form: ax² + bx + c, where a ≠ 0. It's called 'quadratic' from the word 'quadrate' meaning 'square', referring to the x² term. Examples: 2x² …

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A cubic polynomial is a polynomial of degree 3. General form: ax³ + bx² + cx + d, where a ≠ 0. Examples: 2 - x³, x³, √2x³, 3x³ - 2x² + x - 1. The coefficient 'a' of x³ must be non-zero for it to be a …

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p(2) = (2)² - 3(2) - 4 = 4 - 6 - 4 = -6 p(0) = (0)² - 3(0) - 4 = 0 - 0 - 4 = -4 p(-1) = (-1)² - 3(-1) - 4 = 1 + 3 - 4 = 0 Note: Since p(-1) = 0, we say that -1 is a zero of the polynomial.

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A real number k is called a zero of polynomial p(x) if p(k) = 0. For a linear polynomial ax + b, if k is a zero, then ak + b = 0, so k = -b/a. The zero of linear polynomial ax + b is -b/a = -(constant…

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The zero of a linear polynomial ax + b is the x-coordinate of the point where the graph y = ax + b intersects the x-axis. Since the graph of a linear polynomial is a straight line, it intersects the x…