Question

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​

Answer 1

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).