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Consider the expression

(1)/(2)x^(2)+x+7". "
Complete 2 descriptions of the parts of the expression.

The entire expression is a sum with
The coefficients are

Consider the expression\newline12x2+x+7 \frac{1}{2} x^{2}+x+7 \text {. } \newlineComplete 22 descriptions of the parts of the expression.\newline11. The entire expression is a sum with \square.\newline22. The coefficients are \square.

Full solution

Q. Consider the expression\newline12x2+x+7 \frac{1}{2} x^{2}+x+7 \text {. } \newlineComplete 22 descriptions of the parts of the expression.\newline11. The entire expression is a sum with \square.\newline22. The coefficients are \square.
  1. Identify Structure: Identify the structure of the expression.\newlineThe expression 12x2+x+7\frac{1}{2}x^2 + x + 7 is a polynomial in standard form. It is composed of terms that are added together.
  2. Describe Expression: Describe the entire expression.\newlineThe entire expression is a sum of three terms: a quadratic term, a linear term, and a constant term.
  3. Identify Coefficients: Identify the coefficients of the expression.\newlineThe coefficients are the numerical factors that multiply the variable terms. In the quadratic term (1/2)x2(1/2)x^2, the coefficient is 1/21/2. In the linear term xx, the coefficient is 11 (since any number multiplied by 11 is itself). The constant term is 77, which does not multiply a variable, so it is not considered a coefficient in the same sense.

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