Question

What must be added to 2 x to the power 4 minus 5 x to the power 3 + 2 x to the power 2 minus x minus 3 so that the result is exactly divisible by x minus 2

Answer 1

*Question:-

What must be added to 2 x to the power 4 minus 5 x to the power 3 + 2 x to the power 2 minus x minus 3 so that the result is exactly divisible by x minus 2

*Solution:-

Let the required number to be added be k.

Then,

• → p(x) = 2x⁴ = 5x³ + 2x² - x - 3 + k

and

• → g(x) = (x - 2).

Now,

• → g(x) = 0
• → x - 2 = 0
• → x = 2

• →p(2) = 0
• →( 32 - 40 + 8 - 5 + k ) = 0
• →( 32 + 8 - 40 - 5 + k ) = 0
• →( 40 - 45 + k ) = 0
• → ( - 5 + k ) = 0
• → k = 5

Hence the value of the k = 5.

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