Issue with factoring a quadratic

[yme]

I am having a problem with factoring a quadratic with leading coefficient greater than 1

10w^2 + 11w - 6

10w^2 +(-4 + 15)w - 6

10w^2 - 4w + 15w - 6

that is as far as I can go because I do not understand how to proceed

thank you for any help you can provide

 

[Mrspi]

I am having a problem with factoring a quadratic with leading coefficient greater than 1

10w^2 + 11w - 6

10w^2 +(-4 + 15)w - 6

10w^2 - 4w + 15w - 6

that is as far as I can go because I do not understand how to proceed

thank you for any help you can provide

The first two terms have a common factor of 2w. The last two terms have a common factor of 3. Remove the common factor from each pair of terms:

2w(5w - 2) + 3(5w - 2)

Now....you have a common factor of (5w - 2) in each term. Remove that common factor, and put what is left from each term inside a second set of parentheses:

(5w - 2)(2w + 3)

That's your factorization, as you can verify by multiplying the two factors together.

I hope this helps you.

 

[yme]

That was very helpful, thank you.

 

[stapel]

10w^2 - 4w + 15w - 6

that is as far as I can go....

Remove the common factor from each pair of terms:

2w(5w - 2) + 3(5w - 2)

(5w - 2)(2w + 3)

That's your factorization....

Note: You can do it the other way' round, too:

. . . . .10w² + 15w - 4w - 6

. . . . .5w(2w + 3) - 2(2w + 3)

. . . . .(2w + 3)(5w - 2)

So you'd actually done the "hard" part (finding the right way to break up the middle term). Follow this by factoring "in pairs", pull the common factor out front, group the remaining terms, and you're done.

Eliz.