Use synthetic division to find ƒ(2). ƒ(x)=2x3-3x2+7x-12

Ch. 3 - Polynomial and Rational Functions

Lial13th EditionCollege AlgebraISBN: 9780136881063당신이 사용하는 게 아니라요?교과서 변경

모든 교과서

Lial 13th Edition

Ch. 3 - Polynomial and Rational Functions

문제 16

4장, 문제 16

Use synthetic division to find ƒ(2). ƒ(x)=2x³-3x²+7x-12

검증된 단계별 안내

Identify the divisor for synthetic division. Since we want to find ƒ(2), the divisor is \( x - 2 \).

Write down the coefficients of the polynomial \( ƒ(x) = 2x^3 - 3x^2 + 7x - 12 \). These are \( 2, -3, 7, -12 \).

Set up synthetic division by placing the number 2 (from \( x - 2 \)) to the left and the coefficients in a row to the right.

Perform synthetic division by bringing down the first coefficient, multiplying it by 2, adding the result to the next coefficient, and repeating this process across all coefficients.

The final number obtained after completing synthetic division is the value of \( ƒ(2) \).

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

도움이 되었나요?

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Synthetic Division

Synthetic division is a shortcut method for dividing a polynomial by a linear binomial of the form (x - c). It simplifies the long division process by using only the coefficients of the polynomial, making calculations faster and less error-prone.

Evaluating Polynomials Using Synthetic Division

When dividing a polynomial by (x - c), the remainder of the synthetic division equals the value of the polynomial evaluated at x = c. This allows synthetic division to be used as a tool for quickly finding ƒ(c) without direct substitution.

Polynomial Coefficients and Setup

To perform synthetic division, list the coefficients of the polynomial in descending order of degree. If any terms are missing, include a zero coefficient. Proper setup ensures accurate computation of the division and evaluation.