P(x)=x 4
−2x 3
+kx−4P, left parenthesis, x, right parenthesis, equals, x, start superscript, 4, end superscript, minus, 2, x, cubed, plus, k, x, minus, 4 where kkk is an unknown integer.
P(x)P(x)P, left parenthesis, x, right parenthesis divided by (x-1)(x−1)left parenthesis, x, minus, 1, right parenthesis has a remainder of 000.
What is the value of kkk?
Answers
Given : P(x) = x⁴ - 2x³ + kx - 4 dividing by x - 1 leaves remainder 0
To find : Value of k
Solution:
P(x) = x⁴ - 2x³ + kx - 4
When divided by x - 1 leaves remainder 0
=> x - 1 is a factor => x = 1 is one of the root/zero
=> P(1) = 0
=> 1⁴ - 2(1)³ + k(1) - 4 = 0
=> 1 - 2 + k - 4 = 0
=> k - 5 = 0
=> k = 5
Value of k = 5
x⁴ - 2x³ + 5x - 4 = (x - 1)(x³ - x² - x + 4)
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Answer:
The answer is: 5
Its the one on Khan Academy right?
Step-by-step explanation:
