Question
Real Tutor Solution
Tutor-Verified Answer
Answer
\( P(-2) = 0 \)
Solution
การประเมินค่า \( P(a) \) เมื่อ \( P(x) = x^{3} - 2x^{2} - 2x + 12 \) และ \( a = -2 \)
เราต้องการหา \( P(-2) \)
\[
P(-2) = (-2)^{3} - 2(-2)^{2} - 2(-2) + 12
\]
คำนวณทีละขั้นตอน:
1. คำนวณ \( (-2)^{3} \):
\[
(-2)^{3} = -8
\]
2. คำนวณ \( -2(-2)^{2} \):
\[
(-2)^{2} = 4 \\
-2 \times 4 = -8
\]
3. คำนวณ \( -2(-2) \):
\[
-2 \times (-2) = 4
\]
4. รวมค่าทั้งหมด:
\[
P(-2) = -8 - 8 + 4 + 12
\]
5. บวกและลบค่าตามลำดับ:
\[
-8 - 8 = -16 \\
4 + 12 = 16 \\
-16 + 16 = 0
\]
ดังนั้น,
\[
P(-2) = 0
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Bonus Knowledge
To find the value of \( P(-2) \) for the polynomial \( P(x) = x^3 - 2x^2 - 2x + 12 \), simply substitute \( x = -2 \) into the polynomial: \[ P(-2) = (-2)^3 - 2(-2)^2 - 2(-2) + 12 \] Calculating each term gives: \[ P(-2) = -8 - 2(4) + 4 + 12 = -8 - 8 + 4 + 12 = 0 \] So, \( P(-2) = 0 \). This means that \( x + 2 \) is a factor of the polynomial \( P(x) \). Now for the second part, the polynomial can be factored further using synthetic division or polynomial long division to find the other factors.
