Expert: Ahmed Salami - 7/14/2010

Question
When asked to solve b^4+2b^2-24=0 - do you factor?  There are also questions that say Factory the following polynomial - that I factored to ((3x+4)(x-1)....what should I do differently for the solve problem?

Answer
Hi Kristi,
Factoring a polynomial is simply writing it as a product of smaller expressions. When you equate a polynomial to zero, it becomes an equation. To solve an equation means finding the value of the variable that satisfies the equation. Now, factoring and solving are not exactly the same thing in context but they are quite related. Its easy to solve an equation when you've factored the polynomial in the equation.
Consider the equation x² - 5x + 6 = 0, solving it means finding the value(s) of x that satisfy the expression. It becomes easier if we can factorize the polynomial x² - 5x + 6 present in the equation.
Now,
x² - 5x + 6 = (x-3)(x-2)
Back to the equation,
x² - 5x + 6 = 0
(x-3)(x-2) = 0
we then conclude that either x-3 = 0 or x-2 = 0 (since any one of the factors being zero satisfies the expression)
So,
x = 3 or 2

You can always get back to me.

Regards