Question

Разложите на множители xa+xb+6a+6b x^3+x^2+x-1 ab-2a-2b+4 x^5+2x^4-x-2 помогите пожалуйста

Answer 1

xa+xb+6a+6b=х(а+b)+6(а+b)=(х+6)(а+b)
x^3+x^2+x-1=х(х+1)+(х³-1)=(х+1)(х+х²-х+1)
ab-2a-2b+4=а(b-2)-2(b-2)=(b-2)(a-2)
x^5+2x^4-x-2=х(х∧4-1)+2(х∧4-1)=(х+2)(х∧4-1)

Answer 2

Factoring the Given Expression

To factor the given expression xa + xb + 6a + 6b + x^3 + x^2 + x - 1 + ab - 2a - 2b + 4 + x^5 + 2x^4 - x - 2, we can start by grouping like terms and then factorizing each group separately.

1. Grouping the terms: - Group 1: xa + xb + 6a + 6b - Group 2: x^3 + x^2 + x - 1 - Group 3: ab - 2a - 2b + 4 - Group 4: x^5 + 2x^4 - x - 2

2. Factorizing each group: - Group 1: x(a + b) + 6(a + b) - Group 2: x^3 + x^2 + x - 1 - Group 3: a(b - 2) - 2(b - 2) - Group 4: x^5 + 2x^4 - x - 2

3. Factored expression: - (a + b)(x + 6) + (b - 2)(a - 2) + (x - 1)(x^2 + 1) + (x^4 + 2x^3 - 1)(x + 2)

Therefore, the factored form of the given expression is (a + b)(x + 6) + (b - 2)(a - 2) + (x - 1)(x^2 + 1) + (x^4 + 2x^3 - 1)(x + 2).