The factorised form of the equation x^3-2x^2-7x+5 is x(x^2-4x+1)+2(x^2-4x+1)+3. How this equation is factorised to that form?
回答 (2)
2016-07-17 1:40 pm
x³ - 2x² - 7x + 5
= (x³ - 4x² + x) - (-4x² + x) - 2x² - 7x + 5
= (x³ - 4x² + x) + 4x² - x - 2x² - 7x + 5
= (x³ - 4x² + x) + 2x² - 8x + 5
= (x³ - 4x² + x) + (2x² - 8x) + 5
= (x³ - 4x² + x) + (2x² - 8x + 2) - 2 + 5
= x(x² - 4x + 1) + 2(x² - 4x + 1) - 3
= (x³ - 4x² + x) - (-4x² + x) - 2x² - 7x + 5
= (x³ - 4x² + x) + 4x² - x - 2x² - 7x + 5
= (x³ - 4x² + x) + 2x² - 8x + 5
= (x³ - 4x² + x) + (2x² - 8x) + 5
= (x³ - 4x² + x) + (2x² - 8x + 2) - 2 + 5
= x(x² - 4x + 1) + 2(x² - 4x + 1) - 3
2016-07-17 1:40 pm
x^3 - 2x^2 - 7x + 5
= (x + 1)^3 - 5(x + 1)^2 + 9
= x(x^2 - 4x + 1) + 2(x^2 - 4x + 1) + 3
= (x + 1)^3 - 5(x + 1)^2 + 9
= x(x^2 - 4x + 1) + 2(x^2 - 4x + 1) + 3
收錄日期: 2021-04-18 15:15:52
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