Question

Розкладіть на множники многочлен 20a3 – 20a2 + 5аДам 20 ну цых штук ​

Answer 1

Відповідь:

5a (4a2 - 4a + 1)

Пояснення:

Виносимо спільний множник за дужки.

Answer 2

Ответ:

Объяснение:

20a³ – 20a² + 5а=5a(4a²-4a+1)=5a(2a-1)²=5a(2a-1)(2a-1)

Answer 3

Factoring a Polynomial:

To factor the polynomial 20a^3 - 20a^2 + 5a, we can start by looking for common factors among the terms.

Factoring Process:

First, let's factor out the greatest common factor, which is 5a: 5a(4a^2 - 4a + 1)

Now, we have factored out the common factor 5a. The expression inside the parentheses is a quadratic trinomial, which we can further factor using the quadratic formula.

Factoring the Quadratic Trinomial:

To factor the quadratic trinomial 4a^2 - 4a + 1, we can use the quadratic formula: a = 4, b = -4, c = 1

The quadratic formula is given by: x = (-b ± √(b^2 - 4ac)) / (2a)

Substituting the values of a, b, and c into the quadratic formula: x = (-(-4) ± √((-4)^2 - 4*4*1)) / (2*4) x = (4 ± √(16 - 16)) / 8 x = (4 ± √0) / 8 x = (4 ± 0) / 8 x = 4 / 8 x = 1/2

So, the quadratic trinomial 4a^2 - 4a + 1 factors into: 5a(2a - 1)^2

Therefore, the factored form of the polynomial 20a^3 - 20a^2 + 5a is: 5a(2a - 1)^2