Consider the equality
$$
a^3 – 5a^2 + 8a -4 = 0
$$
What are the steps to factor this into the following?
$$
(a − 1)(a − 2)^2 = 0
$$
Is there some technique to do this?
[Math] How to factor the equation $a^3 – 5a^2 + 8a -4 = 0$
factoring
factoring
Consider the equality
$$
a^3 – 5a^2 + 8a -4 = 0
$$
What are the steps to factor this into the following?
$$
(a − 1)(a − 2)^2 = 0
$$
Is there some technique to do this?
Best Answer
You have to guess one root, then do long division and then when you are left with second order polynomial, factorize. So lets say we guessed root $a = 1$, then long division by $(a -1)$ gives $a^2-4a + 4$ which you can then factorize to $(a - 2)^2$.
Often with those types of problems(in schools), you can break out a factor of $a$ (not in this case though), and then you are left with a simple quadratic polynomial.
You could also try looking at a plot of the function and see where the roots are, and then do long division until you can do factorization of quadratic polynomial that's left.