Question

1) 3x (x³ - 4x + 6) =2) ( x - 3 ) ( 2 x + 1 ) = ​

Answer 1

1)3x^4 - 12x^2 + 18x
2)2x^2 + x - 6x - 3 = 2x^2 - 5x - 3

Answer 2

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Answer 3

Let's solve each equation step by step:

1. 3x(x³ - 4x + 6)

Expanding the expression, we get: 3x * x³ - 3x * 4x + 3x * 6

Simplifying further: 3x^4 - 12x^2 + 18x

To solve this equation, we set it equal to zero: 3x^4 - 12x^2 + 18x = 0

Now, we can factor out the common factor of x: x(3x^3 - 12x + 18) = 0

We have two possible solutions:

1. x = 0
2. 3x^3 - 12x + 18 = 0

To solve the cubic equation, we can use numerical methods or approximate the roots. Unfortunately, there is no simple algebraic solution for this cubic equation.

2. (x - 3)(2x + 1)

To solve this equation, we set it equal to zero: (x - 3)(2x + 1) = 0

Now we apply the zero product property, which states that if a product of factors is equal to zero, then at least one of the factors must be zero.

Setting each factor to zero: x - 3 = 0 or 2x + 1 = 0

Solving the first equation: x = 3

Solving the second equation: 2x = -1 x = -1/2

So the solutions to the equation are: x = 3 and x = -1/2