Question

Without actual division. Prove that
2x⁴-8x³+3x²+12x-9 is exactly divisible by x²-4x+3

Answer 1

HERE IS YOUR ANSWER:

TAKE THE QUADRATIC EQUATION x²-4x+3 AND FACTORISE IT.

WE GET :x^2-3X-X+3

X(X-3)-1(X-3)

(x-3) (X-1)

HENCE X=3,1.(SINCE THE EQUATION IS QUADRATIC WE GET 2 ROOTS FPR THE EQUATION.)

NOW SUBSTITUTE VALUE OF X THAT IS 3 IN THE GIVEN BI QUADRATIC

2x⁴-8x³+3x²+12x-9

ANS =0

SIMILARLY SUBSTITUTE THE OTHER VALUE OF X THAT IS 1  IN 2x⁴-8x³+3x²+12x-9

WE GET 0 AS THE ANSWER.

HENCE 2x⁴-8x³+3x²+12x-9 is exactly divisible by x²-4x+3 .

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