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Prove that 2x^4 − 6x^3 + 3x^2 + 3x − 2 is exactly divisible by x^2 − 3x + 2 by long division method. plz plz help me |
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Answer» 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 -2If 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) =0Then, 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 thatP(x) is exactly dividible by x² - 3x + 2 |
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