Question

Розкласти на множники многочлени: X³+3x²+3x+9; 4p⁴-9; 5ax²-10ax-bx+2b-x+2; Винести на дужки спільний множник: 40m²n-25mn²+30mn; 2a(x-y)-(y-x); Срочно!!! Пожалуйста даю 100 балов

Answer 1

Ответ:вот

Объяснение:

Answer 2

Factoring Polynomials:

To factor the given polynomials, we need to find the common factors or use factoring techniques. Let's factor each polynomial one by one:

1. X³ + 3x² + 3x + 9: To factor this polynomial, we can use the grouping method. Group the terms in pairs and factor out the common factors from each pair: (x³ + 3x²) + (3x + 9) Factor out the common factor from the first pair: x²(x + 3) Factor out the common factor from the second pair: 3(x + 3) The factored form of the polynomial is: (x + 3)(x² + 3).

2. 4p⁴ - 9: This polynomial is a difference of squares. We can use the formula a² - b² = (a + b)(a - b) to factor it: 4p⁴ - 9 = (2p² + 3)(2p² - 3) The factored form of the polynomial is: (2p² + 3)(2p² - 3).

3. 5ax² - 10ax - bx + 2b - x + 2: To factor this polynomial, we can group the terms and factor out the common factors: (5ax² - 10ax) + (-bx + 2b) + (-x + 2) Factor out the common factor from the first group: 5ax(x - 2) Factor out the common factor from the second group: -b(x - 2) Factor out the common factor from the third group: -(x - 2) The factored form of the polynomial is: (5ax - b)(x - 2).

4. 40m²n - 25mn² + 30mn: To factor this polynomial, we can factor out the common factor, which is mn: 40m²n - 25mn² + 30mn = mn(40m - 25n + 30) The factored form of the polynomial is: mn(40m - 25n + 30).

5. 2a(x - y) - (y - x): To factor this polynomial, we can simplify the expression inside the parentheses: 2a(x - y) - (y - x) = 2a(x - y) - (-1)(x - y) Now, we can factor out the common factor (x - y): (x - y)(2a + 1) The factored form of the polynomial is: (x - y)(2a + 1).

I hope this helps! Let me know if you have any further questions.