Question 570916
Canceling like factors is similar to canceling common factors in a fraction such as 15/24. Pretty straightforward, as long as you cancel the factors correctly.


Factoring helps solve quadratics, as you don't have to use the quadratic formula. If x^2 + bx + c = 0 factors to (x-p)(x-q) = 0, then right away you know that the roots are p and q. However, not all quadratics factor nicely, and you almost have to "recognize" instantly if a quadratic is factorable (by being able to factor the constant term), otherwise the method is useless.


For example, consider the quadratic *[tex \LARGE x^2 + 12x + 35 = 0]. Since 35 = 5*7 and 5+7 = 12, you could factor it like 


*[tex \LARGE (x+5)(x+7) = 0] (check to make sure the coefficients are the same upon expanding). By the zero-product rule, the roots are -5 and -7.


Factoring quadratics with a leading term other than 1 uses a slightly different method; look in your textbook or online for examples.