2x3 + 8x2 + 3x + 12 = (2x3 + 8x2) + (3x + 12) = 2x2(x + 4) + 3(x + 4) = (x + 4)(2x2 + 3) Since you have asked this question I am assuming that you are not yet at a level where you might want (2x2 + 3) factorised into its imaginary factors.
(x + 1) / (2x3 + 3x + 5) --- Can't depict long division here, but you can work this out by seeing if (x + 1) is a factor of (2x3 + 3x + 5). If it is, then the answer will be 1/(the other factor). In this case, that is true. (2x3 + 3x + 5)/(x + 1) = 2x2 - 2x + 5, so the term term above is equal to: 1 / (2x2 - 2x + 5)
2x1 is 2 2x2 is 4 2x3 is 6 2x4 is 8 2x5 is 10 2x6 is 12
Well, 4 is 2X2 and 6 is 2X3 so the number needs two 2s and one 3 :2x2x3=12
6
Rearrange: 4x5 + 6x2 + 6x3 + 9 Group: 2x2 (2x3 + 3) + 3 (2x3 + 3) Simplify to get your answer: (2x2 + 3) (2x3 + 3)
-2x3 + 2x2 + 12x =(-2x) (x2 - x - 6) =(-2x) (x+2) (x-3)
2x3 + 8x2 + 3x + 12 = (2x3 + 8x2) + (3x + 12) = 2x2(x + 4) + 3(x + 4) = (x + 4)(2x2 + 3) Since you have asked this question I am assuming that you are not yet at a level where you might want (2x2 + 3) factorised into its imaginary factors.
Do you want its factorisation? 2x3 + 2x2 - 12x = 2x(x2 + x - 6) = 2x(x + 3)(x - 2).
(-2x3 - 2x2 + 12x) = -2x (x2 + x - 6) = -2x (x + 3) (x - 2)
(x4 - 2x3 + 2x2 + x + 4) / (x2 + x + 1)You can work this out using long division:x2 - 3x + 4___________________________x2 + x + 1 ) x4 - 2x3 + 2x2 + x + 4x4 + x3 + x2-3x3 + x2 + x-3x3 - 3x2 - 3x4x2 + 4x + 44x2 + 4x + 40R∴ x4 - 2x3 + 2x2 + x + 4 = (x2 + x + 1)(x2 - 3x + 4)
whats the answer for -2x^3+2^2+12x
2x3 - 2x2 - x + 1 = 2x2(x -1) - (x - 1) = (x - 1)(2x2 -1) = (x - 1){[(sq. root of 2)(x)]2 -12} = (x - 1)[(sq. root of 2)(x) - 1][(sq. root of 2)(x) + 1]
2x3 + 2x2 = 2x2 * (x + 1)
-2(x^3 + x^2 + 6)
If that's 2x2, the answer is (x + 2)(x2 + 4)
your equation is this... 2x3 + 11x = 6x 2x3 + 5x = 0 x(2x2 + 5) = 0 x = 0 and (5/2)i and -(5/2)i