SOLUTIONS
What is the multiplicity of each of the roots of this graph?
[tex]f(x)=2x^4+12x^3+16x^2-12x-18[/tex]
Factorise f(x) by the options
(a) According to the option we have -3 is a root of so x+3 is a factor
[tex]\frac{2x^4+12x^3+16x^2-12x-18}{x+3}=2x^3+6x^2-2x-6[/tex]
(b) 1 is a root too so x - 1 is a factor
[tex]\frac{2x^3+6x^2-2x-6}{x-1}=2x^2+8x+6[/tex]
[tex]\begin{gathered} 2x^2+8x+6=2(x+3)(x+1) \\ f(x)=2(x+3)^2(x+1)(x-1) \end{gathered}[/tex]
Therefore the correct answer = Option A
