factoring expressions

Question

 

15x²-11x+2

Answer 1

Factor 15x²-11x+2, Step 1 , (3x   )(5x   ), or (15x   )(x    )

what are two numbers you multiply and you get 2, the possibilities are -1 , and-2 or 1, and 2

 

By the foil method using first possibility ( 3x - 1)(5X-2), (3x)(-2)+(-1)(5x) = -6x-5x=-11x which gives the 2nd term

The first term is given (3x)(5x) = 15x², the third term is then (-1)(-2)= 2, summing the terms 15x²-11x+2

 

so ( 3x-1)(5x-2) is the proper factored terms.

 

 

 

Answer 2

15x²-11x+2

Use AC factoring.

 

a = 15

b = -11

c = 2

 

ac = 30   (This is where the name "AC" factoring comes from.)

Find two factors of 30 that add up to -11 (b).

Since 30 is a positive number, both factors will be either positive or negative.

b is negative, so they have to be negative.

 

The factors you need are (-5) + (-6) = -11

Split the x-term into two parts:  -11x → - 5x - 6x

15x² - 5x - 6x +2

Group the first two and the last two terms, then find a common factor in each of those groups.

(15x² - 5x) + (-6x + 2)   Factor 5x out of the first group and (-2) out of the second group.

5x(3x-1) - 2(3x - 1)         The remaining part of the two groups will be the same: (3x-1).

 

Factor (3x-1) out of the two terms. (This is just the distributive property in reverse.) 

(3x - 1)(5x - 2)           ANSWER

 

Notice how I handled the signs when we grouped the terms.  Using a + sign between the groups and keeping the signs of the -6x and +2 as they were lets you deal with minus signs separately in the next step.  Otherwise, it's really easy to make a sign error: forgetting to change the sign on that -2 at the end.