Question

.x⁵ + 3x⁴- 4x²- 12х²​

Answer 1

x^5+3x⁴-4x²-12x²=

=x^5+3x⁴-16x²=

=x²(x³+3x²-16)

Answer 2

It seems like you have provided a polynomial expression:

x⁵ + 3x⁴ - 4x² - 12x²

If you would like to simplify or factor this polynomial expression, let's break it down step by step:

1. Combine like terms: x⁵ + 3x⁴ - 4x² - 12x² = x⁵ + 3x⁴ - 16x²

2. Factor out the common factor, which is x²: x²(x³ + 3x² - 16)

Now, let's see if we can factor the remaining polynomial, x³ + 3x² - 16, further.

3. Try to factor x³ + 3x² - 16: x³ + 3x² - 16 = (x - 2)(x² + 5x + 8)

So, the factored form of the given polynomial is:

x²(x - 2)(x² + 5x + 8)

If you want to find the roots (zeros) of this polynomial, you can set each factor equal to zero and solve for x:

1. x² = 0 => x = 0
2. x - 2 = 0 => x = 2
3. x² + 5x + 8 = 0 => This quadratic equation can be factored as well: (x + 4)(x + 2) = 0 So, x + 4 = 0 => x = -4 And x + 2 = 0 => x = -2

Therefore, the roots of the polynomial are x = 0, x = 2, x = -4, and x = -2.