Question

Find all solutions to the polynomials below. 5x^3+15x^2+12x=-36

Answer 1

one real solution -3
the other 2 are complex

Answer 2

This looks like fun. Ok so maybe we should set the function to 0. Let's add the 36. We'll get 5x^3+15x^2+12x+36=0. The best way to factor this is through grouping pairs. Our first pair will be 5x^3+15x^2 and our second 12x+36. We want to take something out of both. Let's take 5x^2 out of the first one. We will get \[5x ^{2}(x+3)\]
Let's move on the the second one and take 12 out. \[12(x+3)\]
Now look at both. What is similar? Looks like the (x+3). That is one of the factors the other is the pairs we have in front. So this will be ultimately factored as: \[(5x^{2}+12)(x+3)=0\]

Answer 3

Now solve each for 0.