Write the coefficients of :
`(i) x^(2) " in" 3x^(3)-5x^(2)-5x+6 " " (ii) x^(3) " in" 7x^(4)+5x^(3)+3x+7 " " (iii) x^(2) " in" 4x+7 " " (iv) x " in" 3x-2x^(2)+7x^(3)`

Answer

To solve the question, we need to find the coefficients of specific terms in the given polynomials. Let's break it down step by step.

### Solution:

**(i)** Find the coefficient of \( x^2 \) in the polynomial \( 3x^3 - 5x^2 - 5x + 6 \).

1. Identify the term that contains \( x^2 \).
- The term is \( -5x^2 \).
2. The coefficient of \( x^2 \) is the constant multiplied by \( x^2 \).
- Thus, the coefficient is \( -5 \).

**Answer:** The coefficient of \( x^2 \) is \( -5 \).

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**(ii)** Find the coefficient of \( x^3 \) in the polynomial \( 7x^4 + 5x^3 + 3x + 7 \).

1. Identify the term that contains \( x^3 \).
- The term is \( 5x^3 \).
2. The coefficient of \( x^3 \) is the constant multiplied by \( x^3 \).
- Thus, the coefficient is \( 5 \).

**Answer:** The coefficient of \( x^3 \) is \( 5 \).

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**(iii)** Find the coefficient of \( x^2 \) in the polynomial \( 4x + 7 \).

1. Check if there is a term that contains \( x^2 \).
- There is no \( x^2 \) term present in \( 4x + 7 \).
2. Since there is no \( x^2 \) term, we can consider it as \( 0 \times x^2 \).
- Thus, the coefficient is \( 0 \).

**Answer:** The coefficient of \( x^2 \) is \( 0 \).

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**(iv)** Find the coefficient of \( x \) in the polynomial \( 3x - 2x^2 + 7x^3 \).

1. Identify the term that contains \( x \).
- The term is \( 3x \).
2. The coefficient of \( x \) is the constant multiplied by \( x \).
- Thus, the coefficient is \( 3 \).

**Answer:** The coefficient of \( x \) is \( 3 \).

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### Summary of Coefficients:
- (i) Coefficient of \( x^2 \) is \( -5 \).
- (ii) Coefficient of \( x^3 \) is \( 5 \).
- (iii) Coefficient of \( x^2 \) is \( 0 \).
- (iv) Coefficient of \( x \) is \( 3 \).