Math Problem Statement

Use synthetic division to evaluate f(x) = x^3 - 2x^2 + 4x + 3 for x = 2.

Solution

To solve f(2)f(2) for the function f(x)=x32x2+4x+3f(x) = x^3 - 2x^2 + 4x + 3 using synthetic division:

  1. Set up synthetic division: Write the coefficients of the polynomial: 1,2,4,31, -2, 4, 3. The divisor is x2x - 2, so we use 22 for synthetic division.

  2. Perform synthetic division:

    • Bring down the first coefficient (1).
    • Multiply 22 by the value brought down and add to the next coefficient.
    • Repeat this process for all coefficients.

The steps are:

2 |  1   -2    4    3
    |       2    0    8
    -----------------
       1    0    4   11
  1. Interpret the result:
    • The last value in the bottom row is the remainder. For synthetic division, the remainder is f(2)f(2).

Thus, f(2)=11f(2) = 11.

Would you like a breakdown of each step or have additional questions?


Here are 5 related questions:

  1. How is synthetic division related to evaluating polynomials?
  2. What is the significance of the remainder in synthetic division?
  3. How would the process change if the root was x=3x = -3?
  4. Can synthetic division be used for polynomials of higher degrees?
  5. How does synthetic division help in factoring polynomials?

Tip: Synthetic division is also useful for checking if a value is a root of a polynomial!

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Algebra
Polynomials
Synthetic Division

Formulas

Synthetic division process

Theorems

Remainder theorem

Suitable Grade Level

Grades 9-12