C2 2017 6 Edexcel

6)

a) if (x+3) is a factor then factor theorem says that f(-3)=0
f(-3)=-6(-3)^3 -7(-3)^2+40(-3)+21
=162-63-120+21
=0 \therefore (x+3) is a factor

b) -6x^3 -7x^2 +40x+21 = (x+3)(-6x^2 +11x+7)
=(x+3)(7-3x)(2x+1)

c) this is just solving f(2^y)=0 and we know from b) this occurs when
2^y=-3
2^y>0 for all real y \therefore no solution
or 2^y=7/3
y=1.22
or 2^y=-1/2
no solution here

\therefore y=1.22

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