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
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
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