The answer to x4+x3-14x2+4x+6 divided by x-3 is x3+4x2-2x-2
(x + 2)(x^2+4)
64 is the cube of 4 so: x3 + 64 = (x + 4)(x2 - 4x + 16)
(x3 + 3x2 - 2x + 7)/(x + 1) = x2 + 2x - 4 + 11/(x + 1)(multiply x + 1 by x2, and subtract the product from the dividend)1. x2(x + 1) = x3 + x22. (x3 + 3x2 - 2x + 7) - (x3 + x2) = x3 + 3x2 - 2x + 7 - x3 - x2 = 2x2 - 2x + 7(multiply x + 1 by 2x, and subtract the product from 2x2 - 2x + 7)1. 2x(x + 1) = 2x2 + 2x2. (2x2 - 2x + 7) - (2x2 + 2x) = 2x2 - 2x + 7 - 2x2 - 2x = -4x + 7(multiply x + 1 by -4, and subtract the product from -4x + 7)1. -4(x + 1) = -4x - 42. -4x + 7 - (-4x - 4) = -4x + 7 + 4x + 4 = 11(remainder)
Suppose x3-4x = 0. To solve, factor: x3-4x = x(x2-4) = x(x+2)(x-2) = 0 Now, a product equals 0 if and only one or more of the factors equals 0, so set each factor to 0 and solve. The roots are 0,-2 and +2.
x3 + x2 + 4x + 4 = (x2 + 4)(x + 1)
x^3+x^2+4x+4
The answer to x4+x3-14x2+4x+6 divided by x-3 is x3+4x2-2x-2
Dividend: 4x4-x3+17x2+11x+4 Divisor: 4x+3 Quotient: x3-x2+5x-1 Remainder: 7
Dividend: x3+4x2-9x-36 Divisor: x+3 Quotient: x2+x-12
x(x + 4)(x - 4) or x3 - 16x
x3 - 2x2 - 4x + 8 = (x2 - 4)(x - 2) = (x + 2)(x - 2)(x - 2)
(x + 2)(x^2+4)
x3+36 is an algebraic expression
[ x3 - 4x2 + 7x ] / (x) = x2 - 4x + 7
x3 + 6x2 - 4x - 24 = (x + 6)(x2 - 4) = (x + 6)(x + 2)(x - 2)
64 is the cube of 4 so: x3 + 64 = (x + 4)(x2 - 4x + 16)