The factors of this polynomial would be (x + 4)(x + 2)(x - 1).
To find these, you first have to start with long division to find the first factor. If you use x + 4 it would look like this.
[tex] \frac{x^{3} + 5x^{2} + 2x - 8}{x + 4} [/tex] = [tex] x^{2} + x - 2 [/tex]
Now we are left with only [tex] x^{2} + x - 2 [/tex]. We can factor this by looking for numbers that multiply to the last number and add to the middle number. 2 and -2 multiply to -2 and add to 1. Therefore, we'll use those in parenthesis in their place.
(x + 4)(x + 2)(x - 1)
The factors of x³ + 5x² + 2x - 8 are (x - 1), (x + 2) and (x + 4)
To find the factors of x³ + 5x² + 2x - 8, we need to factorize it.
Let f(x) = x³ + 5x² + 2x - 8.
Using the remainder theorem, let x = 1.
So f(1) = 1³ + 5(1)² + 2(1) - 8 = 1 + 5 + 2 - 8 = 8 - 8 = 0
Since f(1) = 0, x - 1 is a factor.
So, we divide x³ + 5x² + 2x - 8 by x - 1.
So, x³ + 5x² + 2x - 8 ÷ x - 1 = x² + 6x + 8
Factorizing x² + 6x + 8, we have
x² + 6x + 8 = x² + 4x + 2x + 8
= x(x + 4) + 2(x + 4)
= (x + 2)(x + 4)
So, x³ + 5x² + 2x - 8 = (x² + 6x + 8)(x - 1)
= (x - 1)(x + 2)(x + 4)
So, the factors of x³ + 5x² + 2x - 8 are (x - 1), (x + 2) and (x + 4)
Learn more about factors of a polynomial here:
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