Mathematics
A polynomial x4 - 13x2 + 36.
Statement 1: x - 2 is a factor of x4 - 13x2 + 36.
Statement 2: (2)4 - 13 x (2)2 + 36 = 0.
option
Both the statements are true.
Both the statements are false.
Statement 1 is true, and statement 2 is false.
Statement 1 is false, and statement 2 is true.
Factorisation
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Answer
Both the statements are true.
Reason
By factor theorem,
(x - a) is a factor of the polynomial f(x), if the remainder i.e. f(a) = 0.
Let, f(x) = x4 - 13x2 + 36
⇒ f(2) = 24 - 13 x 22 + 36
= 16 - 52 + 36
= 0
Since, f(2) = 0,
So, x - 2 is factor of x4 - 13x2 + 36.
∴ Statement 1 is correct.
Also,
⇒ 24 - 13 x 22 + 36 = 0.
∴ Statement 2 is correct.
Hence, option 1 is the correct option.
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