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Classify the following as linear quadrat...

Classify the following as linear quadratic and cubic polynomial :
`(i)x^(3)+x^(2)+3 " "(ii) x^(2)+5 " "(iii) x^(3)-x " " (iv)3x " "(v)x+3`

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To classify the given polynomials as linear, quadratic, or cubic, we need to determine the degree of each polynomial, which is defined by the highest power of the variable \( x \). ### Step-by-Step Solution: 1. **Identify the first polynomial: \( x^3 + x^2 + 3 \)** - The highest power of \( x \) is 3. - **Classification**: This is a **cubic polynomial**. 2. **Identify the second polynomial: \( x^2 + 5 \)** - The highest power of \( x \) is 2. - **Classification**: This is a **quadratic polynomial**. 3. **Identify the third polynomial: \( x^3 - x \)** - The highest power of \( x \) is 3. - **Classification**: This is a **cubic polynomial**. 4. **Identify the fourth polynomial: \( 3x \)** - This can be rewritten as \( 3x^1 \). - The highest power of \( x \) is 1. - **Classification**: This is a **linear polynomial**. 5. **Identify the fifth polynomial: \( x + 3 \)** - This can be rewritten as \( x^1 + 3 \). - The highest power of \( x \) is 1. - **Classification**: This is also a **linear polynomial**. ### Final Classifications: - (i) \( x^3 + x^2 + 3 \) - **Cubic Polynomial** - (ii) \( x^2 + 5 \) - **Quadratic Polynomial** - (iii) \( x^3 - x \) - **Cubic Polynomial** - (iv) \( 3x \) - **Linear Polynomial** - (v) \( x + 3 \) - **Linear Polynomial**
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