Use synthetic division and the Remainder Theorem to find the indicated function value. f(x)=3x³−7x²−2x+5;f(−3)

검증된 단계별 안내

Identify the divisor for synthetic division based on the value at which the function is evaluated. Since we want to find \( f(-3) \), the divisor is \( x - (-3) = x + 3 \).

Set up synthetic division by writing the coefficients of the polynomial \( f(x) = 3x^{3} - 7x^{2} - 2x + 5 \) in order: \( 3, -7, -2, 5 \).

Write \(-3\) (the zero of the divisor \( x + 3 \)) to the left and perform synthetic division: bring down the first coefficient, multiply by \(-3\), add to the next coefficient, and repeat this process for all coefficients.

The final number obtained after completing synthetic division is the remainder, which by the Remainder Theorem equals \( f(-3) \).

Interpret the remainder as the value of the function at \( x = -3 \), which completes the evaluation.

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.

Remainder Theorem

The Remainder Theorem states that when a polynomial f(x) is divided by (x - c), the remainder is equal to f(c). This theorem allows us to find the value of the polynomial at x = c without fully performing the division.

Evaluating Polynomials at a Given Value

Evaluating a polynomial at a specific value means substituting that value for the variable and calculating the result. Using synthetic division and the Remainder Theorem provides an efficient way to find f(c) without direct substitution.

Use synthetic division and the Remainder Theorem to find the indicated function value. f(x)=3x3−7x2−2x+5;f(−3)