Question

Solve by Factoring:

1.) x²- x + 12 = 0

2.) 4x³ + 21x² - 18x = 0

3.) x³- x² - x + 1

Answer 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 (x-1) is a factor.
Reduce the expression to a quadratic by long division.

Answer 2

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(x-1) - 1(x-1)
= (x-1)(x^1 - 1(
= (x-1)(x-1)(x+1) or (x+1)(x-1)^2

Answer 3

Thank you Reiny, I overlooked #1.

Answer 4

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