x3 + 1 = x3 + x2 - x2 - x + x + 1 = x2(x + 1) - x(x + 1) +1(x + 1) = (x + 1)(x2 - x + 1)
x2 + 7x + 6 = (x + 6) (x + 1)
x2 + 7x - 8 = (x + 8)(x - 1)
4(x-1)2(x2+6x+8) and 10(x-1)(x+2)(X2+7x+10)
3x2 + 2x + 3 + x2 + x + 1 = 4x 2+ 3x + 4
x2 + 8x - 9 factors to (x - 1)(x + 9) x2 - 1 factors to (x - 1)(x + 1) The LCM will be (x - 1)(x + 1)(x + 9) or x3 + 9x2 - x - 9 The GCF is (x - 1)
x(x + 4)(x - 4) or x3 - 16x
The factors of x2 are x and x x times x plus 1 = x2 + x
(x2 - x + 1)(x2 + x + 1)
x^3 - 121x
x4 +x2 =x2 (x2+1)
Since x2 - 1 is a multiple of x - 1, it is the LCM of this problem.
X2+3x+x+3=x(x+1)+3(x+1)=(x+3)(x+1)
I take it LCM is the lowest common multiple For the above the only common multiple is 1 you get x=1 1^2 + (8*1) -9 = 0 and 1^2 -1 = 0 Hope this helps
x3 + 1 = x3 + x2 - x2 - x + x + 1 = x2(x + 1) - x(x + 1) +1(x + 1) = (x + 1)(x2 - x + 1)
(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)
(X + 5)(X + 1) FOIL this. X2 + 1X + 5X + 5 Gather terms. X2 + 6X + 5 ----------------------------those were the factors