Question

If x= 1 is a zero of the polynomial function f(x) = 3x³+4x² - 5x-2, which of the following is another zero of f(x)? (6 points)

Answer 1

Answer: x=1 x=-2 x=-1/3

Explanation:

`f(x)=3x^3+4x^2-5x-2\\\\3x^3+4x^2-5x-2=0\\\\3x^3+(-3x^2+7x^2)-5x-2=0\\\\(3x^3-3x^2)+7x^2-5x-2=0\\\\3x^2(x-1)+7x^2+(-7x+2x)-2=0\\\\3x^2(x-1)+(7x^2-7x)+(2x-2)=0\\\\3x^2(x-1)+7x(x-1)+2(x-1)=0\\\\(x-1)(3x^2+7x+2)=0\\\\x-1=0\\\\x=1\\\\3x^2+7x+2=0\\\\3x^2+(6x+x)+2=0\\\\(3x^2+6x)+(x+2)=0\\\\3x(x+2)+(x+2)=0\\\\(x+2)(3x+1)=0\\\\x+2=0\\\\x=-2\\\\3x+1=0\\\\3x=-1\\\\`

Divide both parts of the equation by 3:

`\displaystyle\\x=-(1)/(3)`