Question:
Coordinate (-3,0) lies on the curve with the equation where 'a' is a constant.
Find two possible values of 'a' .
$$ y= (x+a)^3 + 10(x+a)^2 +25(x+a) $$
My initial impression is to expand all the brackets and collect like terms however that doesn't seem practical given the number of terms that are going to be generated from this equation, especially in an exam scenario.
Whats the method to do his?
hint: your equation $$0=(-3+a)^3+10(-3+a)^2+25(-3+a)$$ and then factorizing $$(a-3)\left((a-3)^2+10(a-3)+25\right)=0$$ and this is equivalent to $$0=(a+2)^2(a-3)$$ can you finish?