Math, asked by aa6647023, 1 year ago

what must be subtracted from x power 4 + 2 x cube minus 2 X square + 4 x + 6 to the result is exactly divisible by X square + 2 x minus 3

Answers

Answered by knjroopa
21

Answer:

2 x + 9

Step-by-step explanation:

Given what must be subtracted from x power 4 + 2 x cube minus 2 X square + 4 x + 6 to the result is exactly divisible by X square + 2 x minus 3

So we need to divide the expression, so

x^2 + 2 x - 3 ) x^4 + 2 x^3 - 2 x^2 + 4 x + 6 ( x^2 + 1

                      x^4 + 2 x^3 - 3 x^3

                 -------------------------------------------- subtracting we get

                                            x^2 + 4 x + 6

                                            x^2 + 2 x - 3

                  ----------------------------------------------

                                                    2 x + 9

So we need to subtract 2 x + 9 from the given expression to be exactly divisible by x^2 + 2 x - 3

Answered by amitnrw
23

Answer:

2x + 9

Step-by-step explanation:

what must be subtracted from x power 4 + 2 x cube minus 2 X square + 4 x + 6 to the result is exactly divisible by X square + 2 x minus 3

Let say d is subtracted from

c to make it divisible by x² + 2x + 3

Let say we get quotient = ax² + bx + c

(x² + 2x + 3)(ax² + bx + c ) = x⁴ + 2x³ - 2x² + 4x + 6 - d

=> ax⁴ + (2a+b)x³ +x²(-3a + 2b + c)  + x(2c - 3b) - 3c = x⁴ + 2x³ - 2x² + 4x + 6 - d

Comparing x⁴

a = 1

Comparing x³

2a + b = 2

=> 2(1) + b = 2

=> b = 0

Comparing x²

-3a + 2b + c  = -2

=> -3 + 0 + c = =2

=> c = 1

x(2c - 3b) - 3c  =  4x + 6 - d

=> x(2(1) - 0) - 3(1) = 4x + 6 - d

=> 2x - 3 = 4x + 6 - d

=> d = 2x + 9

2x + 9 must be subtracted

& quotient = x² + 1

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