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If the polynomial P(x) = x^3 - 6x^2 + 11x - 6 has a root at x = 1, what is P(2)?
If the polynomial P(x) = x^3 - 6x^2 + 11x - 6 has a root at x = 1, what is P(2)?
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If the polynomial P(x) = x^3 - 6x^2 + 11x - 6 has a root at x = 1, what is P(2)?
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P(2) = 2^3 - 6(2^2) + 11(2) - 6 = 8 - 24 + 22 - 6 = 0.
Questions & Step-by-step Solutions
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Q: If the polynomial P(x) = x^3 - 6x^2 + 11x - 6 has a root at x = 1, what is P(2)?
Solution:
P(2) = 2^3 - 6(2^2) + 11(2) - 6 = 8 - 24 + 22 - 6 = 0.
Steps: 10
Show Steps
Step 1: Identify the polynomial P(x) = x^3 - 6x^2 + 11x - 6.
Step 2: Substitute x = 2 into the polynomial to find P(2).
Step 3: Calculate 2^3, which is 8.
Step 4: Calculate 6(2^2), which is 6 * 4 = 24.
Step 5: Calculate 11(2), which is 22.
Step 6: Now, combine all the results: P(2) = 8 - 24 + 22 - 6.
Step 7: First, do 8 - 24, which equals -16.
Step 8: Next, add 22 to -16, which equals 6.
Step 9: Finally, subtract 6 from 6, which equals 0.
Step 10: Therefore, P(2) = 0.
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