Pregunta
(10) \( 7-2 m x n \) State the coefficient of the term indicated: (1) \( -3 x^{2}+4 x-3 \) (2) \( -3 x^{2}+4 x-3 \) (the term in \( x \) ) (2) \( (a+b) x^{3}-x^{2} y+x-1 \) (the term in \( x^{2} \) ) (the term in \( x^{3}, x^{2} \)
Ask by Fowler Page. in South Africa
Mar 18,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
- Coefficient of \( x \) in \( -3x^{2} + 4x - 3 \) is \( 4 \).
- Coefficient of \( x^{2} \) in \( (a+b)x^{3} - x^{2}y + x - 1 \) is \( -y \).
- Coefficient of \( x^{3} \) in \( (a+b)x^{3} - x^{2}y + x - 1 \) is \( a + b \).
Solución
Let's break down the problem step by step to find the coefficients of the specified terms in the given expressions.
### Expression 1: \( -3x^{2} + 4x - 3 \)
1. **Identify the term in \( x \)**:
- The term in \( x \) is \( 4x \).
2. **Coefficient of the term in \( x \)**:
- The coefficient is \( 4 \).
### Expression 2: \( (a+b)x^{3} - x^{2}y + x - 1 \)
1. **Identify the term in \( x^{2} \)**:
- The term in \( x^{2} \) is \( -x^{2}y \).
2. **Coefficient of the term in \( x^{2} \)**:
- The coefficient is \( -y \).
3. **Identify the term in \( x^{3} \)**:
- The term in \( x^{3} \) is \( (a+b)x^{3} \).
4. **Coefficient of the term in \( x^{3} \)**:
- The coefficient is \( a + b \).
### Summary of Coefficients:
1. Coefficient of \( x \) in \( -3x^{2} + 4x - 3 \) is \( 4 \).
2. Coefficient of \( x^{2} \) in \( (a+b)x^{3} - x^{2}y + x - 1 \) is \( -y \).
3. Coefficient of \( x^{3} \) in \( (a+b)x^{3} - x^{2}y + x - 1 \) is \( a + b \).
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Como
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The Deep Dive
In the expression \( -3x^{2} + 4x - 3 \), the coefficient of the term in \( x \) is \( 4 \). Coefficients are simply the numerical factors of the variable terms, and here, \( 4 \) is the number multiplying \( x \), making it the coefficient of \( x \). For the expression \( (a+b)x^{3} - x^{2}y + x - 1 \), the coefficient of the term in \( x^{2} \) is \( -1 \) (due to the \( -x^{2}y \)). The coefficient of the term in \( x^{3} \) is \( a + b \), which is the factor multiplying \( x^{3} \) and represents a combination of \( a \) and \( b \).

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