Factor 15x^2 + 7x - 2?

Hi,

I' m going to explain factoring the way that I teach it, which is probably different from what you've done. Try to follow the steps. This method will work on any trinomial.

15x² + 7x - 2 Look for a GCF None this time. If there was one, factor it out. Then temporarily start both parentheses with the first number and variable.

(15x.......)(15x..........) First sign goes in first parentheses.

(15x..+....)(15x..........) Product of signs goes in 2nd parentheses.

(15x..+....)(15x...-.....) <= neg is because pos x neg = negative

Now multiply your first and third numbers together. Ignore their signs - you've already done them. 15 x 2 = 30. So, out to the side list pairs of factors of 30.

30

------

1, 30

2, 15

3, 10

5, 6

Now you want to pick which factors go in your parentheses, using these rules:

If the signs you put on your parentheses are the SAME, find the factors that ADD up to the middle number in the problem.

If the signs you put on your parentheses are the DIFFERENT, find the factors that SUBTRACT to the middle number in the problem. (Note you look at signs in the parentheses, not in the problem.)

(15x..+....)(15x...-.....) Your signs are different, so you want to subtract factors to get 7. Those factors are 3 and 10.

When you put the numbers in the parentheses, the bigger number is pushy - it always goes first. So your factors now are:

(15x..+..10)(15x.-.3)

Now you have to reduce either or both parentheses by dividing each parentheses' terms by the largest possible divisor. In our problem, the first parentheses is divisible by 5 and the second parentheses is divisible by 3.

(15x..+..10)(15x.-.3)

-------------.---------

.......5............3

This reduces to your final factors of

(3x + 2)(5x - 1)

I know that's probably a different pattern for factoring, but it works on every trinomial - no more trial and error!

I hope that helps!! :-)

Basically you need two factors that add up to be 7 and multiply to be -30 (which is the result of multiplying your first term, 15, and the constant, -2)

These two numbers are 10 and -3.

15x^2+7x-2 can be rewritten as 15x^2-3x+10x-2

(15x^2-3x)+(10x-2)

3x(5x-1)+2(5x-1)

(3x+2)(5x-1)

First: multiply the 1st & 3rd term to get -30. find two numbers that give you -30 when multiplied & 7 (2nd term) when added/subtracted. the numbers are (-3 & 10). rewrite the expression with the new middle terms.

15x^2 - 3x + 10x - 2

SEc: rule - with 4 terms, group "like" terms & factor both sets of parenthesis.

(15x^2 - 3x) + (10x - 2)

3x(5x - 1) + 2(5x - 1)

Third: the inner terms have to match - combine the inner term (once) with the outer term.

(5x - 1)(3x + 2) or, (3x+2)(5x-1)

15 x^2 + 7x - 2 = 15 x^2 + 10x -3x - 2

the idea is that the ratio of the first two numbers is equal to the ratio of the next two numbers.

here 15:10 = -3:-2

after doing this we can take common terms together.

15 x^2 + 10x -3x - 2 = 5x(3x + 2) -1(3x + 2) = (3x + 2)(5x - 1)

Rearrange each equation and set each equivalent to 0 - So: 15x2-7x-2=0 Then- (5x+a million)(3x-2)=0 utilising the foil approach. Then, set every time era equivalent to 0. 5x+a million=0 3x-2=0 SO: 5x=-a million 3x=2. Divide the two factors by the numerical coefficients of x So: x=-a million/5 x=2/3. next:6x2-17x+12=0 Then: (3x-4) (2x-3)=0 x=4/3 x=3/2 x2-36=0 (x+6)(x-6)=0 x=-6 x=6 t2-9=0 (t+3)(t-3)=0 t=-3 t=3 9x2+6x+a million=0 (3x+a million)(3x+a million)=0 x=-a million/3 4x2-4x+a million=0 (2x-a million)(2x-a million)=0 x=a million/2

(5x - 1).(3x + 2)

Check

5x.(3x + 2) - 1.(3x + 2)

= 15x² + 10x - 3x - 2

= 15x² + 7x - 2

15x² + 7x - 2 =

(5x-1)(3x+2)

><

15x²+7x-2

(5x-1)(3x+2)

15x^2+7x-2

=>15X^2+10x-3x-2

=>5x(3x+2)-1(3x+2)

=>(5x-1)(3x+2)

(5x-1)(3x+2)

15 factors 1,15 3,5

2 factors 1,2