1.

Factors of y30 – y27 + y24 – 1 are:1. (y – 1)2. (y + 1)3. Both (y – 1) and (y + 1)4. Neither (y – 1) nor (y + 1)

Answer» Correct Answer - Option 1 : (y – 1)

Concept:

If, (x + 1) or (x – 1) are factors of a given equation, then on putting x = 1 or x = (-1) in place of ‘x’ in the given equation will give 0. SO, by using option, put the value ‘y’ in the equation and test if the result comes 0 or not. If not, then it is not the factor of the equation, if yes, then it a factor of the given equation.

Calculation:

If (y – 1) is a factor,

Then, putting y = 1 in the given equation will give 0.

⇒ 130 – 127 + 124 – 1

⇒ 1 – 1 + 1 – 1 = 0

∴ (y – 1) is a factor of the given equation.

Now with (y + 1);

Put y = (-1) in the given equation;

⇒ (-1)30 – (-1)27 + (-1)24 – 1

⇒ 1 + 1 + 1 – 1 = 2

∴ (y + 1) is not a factor of given equation.


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