Question
Asked Nov 9, 2019
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Factor the polynomial function f(x). Then solve the equation f(x)=0.

f(x)= x3+10x2+19x-30

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Expert Answer

Step 1

For x=1 , f(1)=0 so x=1 is a zero of the function f(x)

 

f(x) x3+10x2+19x-30
f(1) 1+10(1)+19(1)-30
f(1) 1+10+19-30
f(1) 0
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f(x) x3+10x2+19x-30 f(1) 1+10(1)+19(1)-30 f(1) 1+10+19-30 f(1) 0

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Step 2

Apply synthetic division to find the other factor. 

Coefficients of x^3+10x^2+19x-30 is 1,10,19,-30. Divide it by x=1

Quotient = x^2+11x+30 

So, f(x)=(x-1)(x^2+11x+30 )

19
30
30
30
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19 30 30 30

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Step 3

Then find the factors of (x^2+11x+30 ).

x^2+11x+30=(...

x2+11x+30
=x2+5x+6x+30
=x(x+5)+6(x+5)
(x+5)(x+6)
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x2+11x+30 =x2+5x+6x+30 =x(x+5)+6(x+5) (x+5)(x+6)

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