Polynomials, SMB-008 Consider the polynomial `P(x) = 2x^4+3x^3-12x^2-7x+6`. Fully factorised, `P(x) = (2x-1)(x+3)(x+a)(x-b)` Find the value of `a` and `b` where `a,b>0`. (3 marks) Show Answers Only `a=1, b=2` Show Worked Solution `text{Test for factors (by trial and error):}` `P(1) = 2+3-12-7+6 = -8` `P(-1) = 2-3-12+7+6 = 0\ \ =>\ \ (x+1)\ \ text{is a factor}` `P(2) = 32+24-48-14+6 = 0\ \ =>\ \ (x-2)\ \ text{is a factor}` `:. a=1, b=2`