Find the value of k such that g(x) a factor of p(x):
p(x) = 2x3 + kx2 + 11x + k + 3, g(x) = 2x – 1;
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46
Answer:
- -7 is the value of k.
Step-by-step explanation:
p(x) = 2x³ + kx² + 11x + k + 3.
g(x) = 2x - 1
When g(x) is divided by p(x).
=> 2x - 1 = 0
=> 2x = 1
=> x = 1/2
p(1/2) = 2(1/2)³ + k(1/2)² + 11(1/2) + k + 3 = 0
=> 2(1/8) + k(1/4) + 11(1/2) + k + 3 = 0
=> 2/8 + k/4 + 11/2 + k + 3 = 0
=> 2 + 2k + 44 + 8k +24/8 = 0
=> 70 + 10k = 0
=> 70 = -10k
=> k = 70/-10
∴ k = -7
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