Select all of the factors of x3 5x2 2x 8

Asked by admin @ 12/10/2021 in Mathematics viewed by 391 People

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

x + 5
x – 3
x + 4
x – 1
x + 3
x + 2

Answered by admin @ 12/10/2021

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.

$\frac{x^{3} + 5x^{2} + 2x - 8}{x + 4}$ = $x^{2} + x - 2$

Now we are left with only $x^{2} + x - 2$ . 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)

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