One factor of f(x) = x^3 + x^2 -22x - 40 is x + 4. Find the other factors.
I got confused on my work but I ended up with x - 6 and x + 1 as the remaining factors
x^3+x^2-22x-40=(x+4)(x^2-3x-10)
=(x+4)(x+2)(x-5)
To find the remaining factors, we can use polynomial division or synthetic division. Let's use synthetic division to divide f(x) by x + 4:
-4 | 1 1 -22 -40
-4 12 40
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1 -3 -10 0
The remainder is 0, which means x + 4 is a factor. The quotient obtained from the division represents the corresponding quadratic expression. In this case, the quotient is 1x^2 - 3x - 10.
Now, let's factor the quadratic expression 1x^2 - 3x - 10. By factoring or using the quadratic formula, we find that the quadratic expression can be factored as (x - 5)(x + 2).
Therefore, the complete set of factors for f(x) = x^3 + x^2 - 22x - 40 is (x + 4)(x - 5)(x + 2).