x3 - 3x2 + x - 3 = (x2 +1)( x - 3)
x3 + 3x2 - 4x -12 x2(x + 3) - 4(x + 3) (x2 - 4)(x+3)
3X^2 + 9X/3X factor out 3X 3X(X + 3)/3X 3X/3X = 1, so... X + 3 is the simplest form here
Find the remainder when f(x) is divided by (x - k) ƒ(x) = 2x3 + 3x2 + 4x + 18; k = -2 (x - k) = (x - (-2)) = (x + 2) x + 2 = 0 x = -2 By Remainder Theorem ƒ(x) = 2x3 + 3x2 + 4x + 18 ƒ(-2) = 2(-2)3 + 3(-2)2 +4(-2) + 18 = 2(-8) + 3(4) + 4(-2) +18 = -16 + 12 -8 +18 = 6 Thus, the remainder is 6
(3x2 - 6x)/3x = 3x(x-2)/3x = x-2, for x<>0
1
x3 - 3x2 + x - 3 = (x2 +1)( x - 3)
x3 - 3x2 + x - 3 = (x - 3)(x2 + 1)
-3x2+10x-3 -(3x2-10x+3) -(3x-1)(x-3)
x3 + ax + 3a + 3x2 = x (x2 + a) + 3 (a + x2) = x (x2 + a) + 3 (x2 + a) = (x2 + a)(x + 3) Checking the work: x3 + ax + 3x2 + 3a or x3 + 3x2 + 3a + ax = x2 (x + 3) + a (3 + x) = x2 (x + 3) + a (x + 3) = (x + 3)(x2 + a)
3x2-2x-21 = (3x+7)(x-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(x - 3)(x + 3)
The answer is 3.
3x2 + 48 + 192 = 3x2 + 240 = 3 (x2+ 80)
3x2 + 10x + 3 = (x + 3)(3x + 1).
-3(x + 3)(x + 3)