Problem 51 - College Algebra

Question

State the Remainder Theorem.

Step-by-Step Solution

Answer

The Remainder Theorem states that if a polynomial \(f(x)\) is divided by \((x-a)\), then the remainder is \(f(a)\)

Step 1: State the Remainder Theorem

The Remainder Theorem states: If a polynomial \(f(x)\) is divided by \((x-a)\), then the remainder is \(f(a)\). Essentially, this theorem is saying that if you divide a polynomial by a binomial of form \(x-a\), you'll get the same remainder as if you evaluated the function at \(x = a\).

Step 2: Identify the algebraic structure

Determine the type of algebraic problem.

Step 3: Apply algebraic techniques

Use factoring, expanding, or systematic methods.

Step 4: Simplify and solve

Simplify expressions and solve for unknowns.

Step 5: State the result

Write the final answer.

Step 6: Conclude with the answer

The Remainder Theorem states that if a polynomial \(f(x)\) is divided by \((x-a)\), then the remainder is \(f(a)\)