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Q: Factor x3 plus 4x2 plus x plus 4?

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x3 + 4x2 + 6x + 24 = (x2 + 6)(x + 4)

(x - 2)(x + 4)(x - 6)

(x3 + 4x2 - 3x - 12)/(x2 - 3) = x + 4(multiply x2 - 3 by x, and subtract the product from the dividend)1. x(x2 - 3) = x3 - 3x = x3 + 0x2 - 3x2. (x3 + 4x2 - 3x - 12) - (x3 + 0x2 - 3x) = x3 + 4x2 - 3x - 12 - x3 + 3x = 4x2 - 12(multiply x2 - 3 by 4, and subtract the product from 4x2 - 12)1. 4x(x - 3) = 4x2 - 12 = 4x2 - 122. (4x2 - 12) - (4x2 - 12) = 4x2 - 12 - 4x2 + 12 = 0(remainder)

x3 - 4x2 + 5x - 20 = x2*(x - 4) + 5*(x - 4) = (x2 + 5)*(x - 4)

x3 + 4x2 - 16x - 64 = (x + 4)(x + 4)(x - 4).

It is not possible to be sure about the answer because there is no sign before the linear term. If the polynomial is x3-4x2+x-4 then, the factors are (x-4) and (x2+1).

x3 + x2 + 4x + 4 = (x2 + 4)(x + 1)

4(x + 1)(x + 1)

x3 + 4x2 + 16x + 64 =x2*(x + 4) + 16(x + 4) = (x + 4)*(x2 + 16) which has no further real factors.

4(x^2 + 2x + 8)

4(x + 2)(x + 2)

4(x + 2)(x + 1)