Question

homework assignment # 6
category: quiz
current score:
4/25 points
current learning objective: evaluating a polynomial using the remainder theorem
question 6
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the value of ( x ^ { 3 } + 14 x ^ { 2 } - 77 x + 21 ) when ( x = 4 ) is
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Explanation:

Step1: Substitute \(x = 4\) into the polynomial

Substitute \(x = 4\) into \(x^{3}+14x^{2}-77x + 21\), we get \(4^{3}+14\times4^{2}-77\times4 + 21\).

Step2: Calculate each term

• Calculate \(4^{3}=4\times4\times4 = 64\).
• Calculate \(14\times4^{2}=14\times16 = 224\).
• Calculate \(77\times4 = 308\).

Step3: Compute the result

$$
LATEXBLOCK0
$$

So the value of \(x^{3}+14x^{2}-77x + 21\) when \(x = 4\) is \(1\).

Answer:

$125$