Questions: Use synthetic division and the Remainder Theorem to find the indicated function value. f(x)=6x^3-4x^2-5x+6 ; f(-3) f(-3)=

Use synthetic division and the Remainder Theorem to find the indicated function value. f(x)=6x^3-4x^2-5x+6 ; f(-3) f(-3)=
Transcript text: Use synthetic division and the Remainder Theorem to find the indicated function value. \[ \begin{array}{l} f(x)=6 x^{3}-4 x^{2}-5 x+6 ; f(-3) \\ f(-3)=\square \end{array} \]
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Solution

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Solution Steps

Step 1: Write down the coefficients of the polynomial

The coefficients are [6, -4, -5, 6].

Step 2: Perform Synthetic Division

Perform synthetic division by dividing the polynomial by \(x + 3 \).

Step 3: Calculate the Remainder

The remainder obtained from the synthetic division is the value of the polynomial at \(x = -3 \), which is \(f( -3 ) = -177 \).

Final Answer:

The value of the polynomial at \(x = -3\) is \(f(-3) = -177\).

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