Ответы на вопрос:
1) p(x) = x^2 + 3x + 4; q(x) = x - 2 p(x) = x^2 - 4x + 4 + 4x - 4 + 3x + 4 = (x-2)^2 + 7x = (x-2)^2 + 7(x-2) + 14 = = (x - 2)*(x - 2 + 7) + 14 = (x - 2)(x + 5) + 14 3) p(x) = 6x^3 + 3x^2 - 4x + 3; q(x) = 2x + 1 p(x) = 6/8*(8x^3 + 3*4x^2 + 3*2x + 1) - 6/8*12x^2 - 6/8*6x - 6/8 + 3x^2 - 4x + 3 = 3/4*(2x+1)^3 - 9x^2 - 9/2*x - 3/4 + 3x^2 - 4x + 3 = = 3/4*(2x+1)^3 - 6x^2 - 17/2*x + 9/4 = = 3/4*(2x+1)^3 - 3/2*(4x^2 + 4x + 1) + 6x + 3/2 - 17/2*x + 9/4 = = 3/4*(2x+1)^3 - 3/2*(2x+1)^2 - 5/2*x + 15/4 = = 3/4*(2x+1)^3 - 3/2*(2x+1)^2 - 5/4*(2x+1) + 5/4 + 15/4 = = 3/4*(2x+1)^3 - 3/2*(2x+1)^2 - 5/4*(2x+1) + 5 = = 1/4*(2x + 1)*(2(2x+1)^2 - 6(2x+1) - 5) + 5 можно во второй скобке. 4) p(x) = 2x^3 - 3x^2 + 2x - 2; q(x) = x^2 + 2 p(x) = 2(x^3 + 2x) - 4x - 3x^2 + 2x - 2 = = 2x*(x^2+2) - 3x^2 - 2x - 2 = 2x*(x^2+2) - 3(x^2+2) - 2x - 2 + 6 = = (x^2 + 2)*(2x - 3) - 2x + 4
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