Question

Give the constant term, $a_{0}$. $$ t(t-1)(t-2) $$

   Give the constant term, $a_{0}$.
$$
t(t-1)(t-2)
$$

Algebra Form and Function

Algebra Form and Function

William G. McCallum,… 1st Edition

Chapter 12, Problem 10

Instant Answer

Solved by Expert Nick Johnson

04/12/2022

Step 1

We have $(t-1)(t-2)$ which can be expanded as $t^2 - 3t + 2$. Show more…

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Give the constant term, $a_{0}$. $$ t(t-1)(t-2) $$

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Key Concepts

Evaluation at Zero

Evaluation at zero is a technique used in polynomial analysis where the polynomial is substituted with zero for the variable. Since all terms with a factor of the variable become zero, the result of this evaluation is precisely the constant term. This method is a straightforward way to extract the coefficient of the zero degree term.

Polynomial Expansion

Polynomial expansion is the process of multiplying out expressions that involve polynomials to write them in a standard form where like terms are combined. This procedure is essential for identifying specific coefficients, such as the constant term, and for simplifying the expression to analyze its properties.

Polynomial

A polynomial is an expression consisting of variables (indeterminates) and coefficients, combined using only addition, subtraction, multiplication, and non-negative integer exponents. Polynomials are fundamental objects in algebra and are used to model various phenomena and solve equations.

Constant Term

The constant term in a polynomial is the term that does not contain any variables; it is essentially the coefficient of the x^0 term. This term can be determined by evaluating the polynomial when all variables are set to zero, and it plays an important role in understanding the behavior of the polynomial at that point.

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