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If f(x) = x^3 + 8x² + 11x-20 and x+5 is a factor of f(x), then find all of the zeros of f(x) algebraically

If Fx X3 8x 11x20 And X5 Is A Factor Of Fx Then Find All Of The Zeros Of Fx Algebraically class=

Sagot :

Answer:

The zeros are (-5,-4,-1)

Step-by-step explanation:

Since we have a linear factor, we can use the method of long division to get the other factors

What this mean is that we simply divide the polynomial by the linear expression

we have this division result as;

By dividing, we have the other factor as ;

x^2 + 3x - 4

so we simply factorize this

x^2 -x + 4x - 4

x(x-1) + 4(x-1)

(x + 4)(x-1)

So the complete factors are;

(x + 5)(x + 4)(x-1)

To get the zeros, we simply equate each of the terms to zero

and we have our answer as;

-5 , -4 , 1

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