Question

show that 2 x ki power 4 - 6 x ki power 3 + 3 x ki power 2 + 3 x minus 2 is exactlydivisible by X ki power 2 - 3 x +2​

Answer 1

Answer:

the process by which green plants and some other organisms use sunlight to synthesize nutrients from carbon dioxide and water. Photosynthesis in plants generally involves the green pigment chlorophyll and generates oxygen as a by-product.

Answer 2

SOLUTION-

• First we factorize divisor x² - 3x+2

• = x² -2x - x +2 = x(x-2) -1 ( x - 2)

• = ( x-2) (x-1)

• Now, dividend p(x) = 2x^4 - 6x^3 + 3x² + 3x -2

• If p(x) is dividible by ( x-2) & (x-1) each, then p(x) is also divisible by its product.

• & by remainder theorem , if p(2) = 0 & p(1) =0

• Then, p(x) is divisible by the divisor.

• P( 2) = 2* 2^4 - 6* 2^3 + 3* 2² + 3*2 -2

• = 32 - 48 + 12 + 6 - 2 = 50 - 50

• = 0 ….. (1)

• Also p(1) = 2* 1^4 - 6* 1^3 + 3 *1² + 3*1 -2

• = 2 - 6 +3 + 3 - 2

• = 0 ….. (2).

• By (1) & (2), we can conclude that

• P(x) is exactly dividible by x² - 3x + 2