Select all of the factors of x3 + 5x2 + 2x – 8. x + 5 x – 3 x + 4 x – 1 x + 3 x + 2

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.

=

Now we are left with only . 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:

link