12th grade  Math
posted by Eliza on .
Solve by Factoring:
1.) x² x + 12 = 0
2.) 4x³ + 21x²  18x = 0
3.) x³ x²  x + 1

1.
Factor by completing the square or the quadratic formula.
However, factoring by trial and error is faster, noting that only a few rational factors are possible, namely x±1, x±2, x±3, x±4, x±6.
2. note that x is a common factor of all the terms, so the problem reduces to a quadratic expression.
3. The sum of the coeffients is zero implies that (x1) is a factor.
Reduce the expression to a quadratic by long division. 
factoring usually assumes we are dealing with rational numbers
x^2  x + 12 = 0 does not factor (there are no two numbers which multiply to get 12 and add to get 1)
2. x(4x^2 + 21x  18)
= x(4x  3)(x + 6)
3. grouping
x^2(x1)  1(x1)
= (x1)(x^1  1(
= (x1)(x1)(x+1) or (x+1)(x1)^2 
Thank you Reiny, I overlooked #1.

1x1=1x10000+9+9+9=10027