Quotient: 2x3-x2-14x+42 Remainder: -131 over (x+3)
2/3 + 2/12 = [ 2x4 + 2 ]/12 = 10/12 = 5/6
Plus 3.
2x4 - 9x3 + 13x2 - 15x + 9 = 2x4 - 6x3 - 3x3 + 9x2 + 4x2 - 12x - 3x + 9 = 2x3(x - 3) - 3x2(x - 3) + 4x(x - 3) - 3(x - 3) = (x - 3)*(2x3 - 3x2 + 4x - 3) So the quotient is (2x3 - 3x2 + 4x - 3) and the remainder is 0.
-3
you put the fraction in simplest form (the numerator and denominator have no common factors besides one) then you find what number your variable should be to make the denominator 0. this is excluded value b/c your denominator can never equal 0 the number you found is your excluded value ex. 4 ------ Your excluded value is 3 because 3(3-3)=0 x(x-3)
2x4 - 7x3 + x2 + 7x - 3 = (x + 1)(2x3 - 9x2 + 10x - 3) = (x + 1)(x - 1)(2x2 -7x + 3) = (x + 1)(x - 1)(x - 3)(2x -1)
You can work this out with long division, by checking to see if (x2 - 1) is a factor of (2x4 + 4x3 - x2 + 4x - 3). It is. Unfortunately, the WikiAnswers system is somewhat limited in depicting things such as long division, so we won't be able to represent it here. In short though, (2x4 + 4x3 - x2 + 4x - 3) / (x2 + 1) is equal to 2x2 + 4x - 3. which means that: (x2 + 1) / (2x4 + 4x3 - x2 + 4x - 3) = (x2 + 1) / (x2 + 1)(2x2 + 4x - 3) = 1 / (2x2 + 4x - 3)
Quotient: 2x3-x2-14x+42 Remainder: -131 over (x+3)
2x^3 - 3x^2 + 4x - 3
There are several simplifications. Each of these is a different way of stating the same value: 8 2x4 4x2 2^3
2/3 + 2/12 = [ 2x4 + 2 ]/12 = 10/12 = 5/6
Plus 3.
2x4 - 9x3 + 13x2 - 15x + 9 = 2x4 - 6x3 - 3x3 + 9x2 + 4x2 - 12x - 3x + 9 = 2x3(x - 3) - 3x2(x - 3) + 4x(x - 3) - 3(x - 3) = (x - 3)*(2x3 - 3x2 + 4x - 3) So the quotient is (2x3 - 3x2 + 4x - 3) and the remainder is 0.
11
3
1 + 3 = 4