Question - Determining Polynomial Expressions

Solution:

(a) \( x^2 - 5 \) is a quadratic expression because it can be written in the form \( ax^2 + bx + c \) with \( a = 1, b = 0, c = -5 \).

(b) \( 2x^2 + x \) is a quadratic expression because it can be expressed as \( ax^2 + bx + c \) with \( a = 2, b = 1, c = 0 \).

(c) \( 3x^2 - 3x + 1 \) is a quadratic expression since it conforms to the standard form \( ax^2 + bx + c \) with \( a = 3, b = -3, c = 1 \).

(d) \( x^4 - 2x - 1 \) is not a quadratic expression as it has a degree of 4, which exceeds 2.

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