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Question
Determine which of the following polynomials has x – 2 a factor:
3x2 + 6x – 24
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Solution
According to the question,
Let p(x) = 3x2 + 6x − 24 and g(x) = x – 2
g(x) = x – 2
Zero of g(x)
⇒ g(x) = 0
x – 2 = 0
x = 2
Therefore, zero of g(x) = 2
So, substituting the value of x in p(x), we get,
p(2) = 3(2)2 + 6(2) – 24
= 12 + 12 – 24
= 0
Since, the remainder = zero,
We can say that,
g(x) = x – 2 is factor of p(x) = 3x2 + 6x − 24
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