Factor: 3x^2 - 11x + 6
Kasey
by inspection: (3x - 2)(x - 3)
by method:
Step 1:
take the first terms times the last term. we get 18x^2
take the middle term, we have -11x
Step 2:
now think of two numbers that when multiplied gives 18x^2 and when added gives -11x
the numbers are: -2x and -9x
Step 3:
rewrite the quadratic, this time writing the middle term in terms of these two numbers, we get:
3x^2 - 9x - 2x + 6
Step 4:
factor by grouping:
we have 3x common to the first two terms and -2 common to the last two, so we get:
3x(x - 3) - 2(x - 3) ........factor out the common (x - 3)
= (x - 3)(3x - 2)
when the coefficient of x^2 is small, like 2,3,4,5,6,7, or prime, you should be able to use inspection to figure the factors out, since there will not be many candidates for the first positions in the brackets. the method i gave you is for when you have larger numbers.