Разложите на линейные множители многочлен: 1) x ^ 3 - 2x ^ 2 - x + 2 ; 2) x^ 4 -13x^ 2 +36; 3) x ^ 3 - 3x ^ 2 - 4x + 12
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Ответы на вопрос:
Объяснение:
1) x3–2x2–x+2=(x3–2x2)+(–x+2)=x2(x–2)–(x–2)=(x–2)(x2–1)=
=(x–2)(x–1)(x+1).
2) x4–13x2+36=(x4–4x2)+(–9x2+36)=x2(x2–4)–9(x2–4)=
=(x2–4)(x2–9)=(x–2)(x+2)(x–3)(x+3).
3) x3–3x2–4x+12=(x3–3x2)+(–4x+12)=x2(x–3)–4(x–3)=(x–3)(x2–4)=
=(x–3)(x–2)(x+2).
См правило внутри =============================== a1/a2 = b1/b2 = c1/c2 - 3x + ay + 6 = 0 9x - 3y - 18 = 0 - 3/9 = a/-3 = 6/-18 - 1/3 = - a/3 = - 1/3 следовательно, а = 1
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