# Math Help - Factorising Quadratics????

Hey Can someone please explain to me how to factorisequadratics when the have no common factor??????

e.g 3x^2-7x-6

If would help if you could give more then one way of solving it cause i'm really slow at catching on hahaha There are some bits i understand but the I get all confused with the minuses and pluses.

Make as many sugestions as you like

Thanks

2. The first thing that you should notice is that the coefficient of the leading term is greater than 1, in this case, it's 3.

$3x^2-7x-6$

You will need to factor by grouping, to do this use to following steps.

$ax^2+bx+c$

Step 1: If a > 1, multiply 'a' times 'c'.
Step 2:Find two numbers whose sum is equal to 'b' and whose product is equal to 'ac'.
Step 3: Rewrite your equation as $(ax^2+n_{1}x)+(n_{2}x+c)$ where $n_{1}$ and $n_{2}$ are the numbers that you found in Step 2. Tip: Look at the numbers that you've found and group them wisely, this will aid in factoring. You'll see what I mean below.
Step 4: Factor both groups independently. This will leave you with two terms with a binomial factor in common.
Step 5: Factor out the binomial.

EXAMPLE:
$3x^2-7x-6$ The original quadratic.
$3*-6 = -18$ Multiply a*c
Two numbers that add to be -7 and multiply to be -18 are -9 and 2.
$(3x^2-9x)+(2x-6)$ Rewrite using our two numbers. Notice how 3 is a factor of 9 and 2 is a factor of 6? We could have written it the other way but it would have been more work to factor.
$3x(x-3)+2(x-3)$ Factor the two groups independently. See how both terms now have the common factor $(x-3)$
$(x-3)(3x+2)$ Factor out $(x-3)$

3. Originally Posted by Soapy123
Hey Can someone please explain to me how to factorisequadratics when the have no common factor??????

e.g 3x^2-7x-6

If would help if you could give more then one way of solving it cause i'm really slow at catching on hahaha There are some bits i understand but the I get all confused with the minuses and pluses.

Make as many sugestions as you like

Thanks
(3x+2)(x-3)

you'll need a to factor 3x^2 that means (3x)(x), then multiply a and c that will be -18 find a factor that add up to -7 that will be -9 and 2.
since 3x*-3 is -9 and 2*-3 is -6 you will use -3
if the the middle term is negative that means the first inner term and the last outer term is positive and negative. if the middle term is postive say for example, 3x^2+3x-6 and the last term=c is negative it means that the bigger factor is positive 3 and -2 hence (3x-3)(x+2)

sometimes in factoring i used trial and error to know if which is positive an negative.

4. Hmm, not sure what happened but an edit turned into a new post. Not sure how to delete posts on this forum.

5. Originally Posted by Scientia
Hmm, not sure what happened but an edit turned into a new post. Not sure how to delete posts on this forum.
In case you have posted the same question twice report the same by clicking on on the upper right side of your post and write that you have posted it twice ... Anyway try to avoid it by not clicking on "Submit Post" twice