Factor:
27X^2-90X+27
27 factors into 9*3. How can 9*3 from each end term be combined to give you -90 for the center term?
27X^2-90X+27
are you sure it is not
27X^2-30X+27? as I have done this one recently
take out a factor of 3
3(9x^2-10x+9)
then by inspection
3(x-1)(x-9) = 27x^2-30x+27
if it is
27X^2-90X+27
then take out 9
9(3x^2-10x+3)
then by inspection
9(x-1/3)(x-3)
To your original formula:
27X^2-90X+27 = (9X-3)(3X-9)
To factor the expression 27X^2 - 90X + 27, we can use the method of factoring by grouping.
Step 1: Group the first two terms and the last two terms separately.
(27X^2 - 90X) + (27)
Step 2: Find the greatest common factor (GCF) of each group.
For the first group (27X^2 - 90X), the GCF is 9X:
9X(3X - 10)
For the second group (27), the GCF is 27:
27(1)
Step 3: Factor out the GCF from each group.
9X(3X - 10) + 27(1)
Step 4: Notice that we can further simplify the expression by factoring out a common factor from both terms. In this case, the common factor is 3.
3(3X - 10) + 27(1)
Step 5: Finally, simplify the expression by distributing the common factor (3).
3(3X - 10) + 27
The fully factored expression is:
3(3X - 10) + 27