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Consider the expression

4x^(2)+x+3". "
Complete 2 descriptions of the parts of the expression.

The entire expression is a sum with
The coefficients are

Consider the expression\newline4x2+x+3 4 x^{2}+x+3 \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\newline4x2+x+3 4 x^{2}+x+3 \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. Polynomial Standard Form: The expression 4x2+x+34x^{2}+x+3 is a polynomial in standard form. The standard form of a polynomial is when the terms are ordered from the highest degree to the lowest degree. In this case, the term with the highest degree is 4x24x^{2}, followed by xx, and then the constant term 33.
  2. Sum of Terms: The entire expression is a sum of three terms: 4x24x^{2}, xx, and 33. Each term is added together to form the polynomial.
  3. Coefficients Explanation: The coefficients in a polynomial are the numerical factors that multiply the variable terms. In the expression 4x2+x+34x^{2}+x+3, the coefficient of the term 4x24x^{2} is 44, the coefficient of the term xx is 11 (since any number multiplied by 11 is itself, the coefficient is implied), and the constant term 33 can also be considered a coefficient, specifically of the term 0x0x or x0x^{0}.