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Factor the polynomial function f(x). Then solve the equation f(x)=0.
f(x)= x3+10x2+19x-30
Expert Answer
For x=1 , f(1)=0 so x=1 is a zero of the function f(x)
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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
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 )
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19 30 30 30
Then find the factors of (x^2+11x+30 ).
x^2+11x+30=(...
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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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