Factoring confuses me?

Question

how would you factor this? I cant factor! :(

3(2a-b)^2+17(2a-b)+10

Answer 1

3(2a - b)^2 + 17(2a - b) + 10

First simplify the (2a - b) by letting it equal x.

= 3x^2 + 17x + 10

Work out the factors of 3. They are 1 * 3.
That means the expression will look like : (x + ...)(3x + ...)

Now work out the factors of 10. They are 1 * 10 or 2 * 5.
The expression will now be one of these four possibilities :

(x + 1)(3x + 10)
(x + 10)(3x + 1)
(x + 2)(3x + 5)
(x + 5)(3x + 2)

Now multiply out the x's and see which one comes to 17.

(x + 1)(3x + 10) gives : 3x + 10x = 13x (incorrect)
(x + 10)(3x + 1) gives : x + 30x = 31x (incorrect)
(x + 2)(3x + 5) gives : 5x + 6x = 11x (incorrect)
(x + 5)(3x + 2) gives : 2x + 15x = 17x (this is the one)

So, 3x^2 + 17x + 10 factors to (x + 5)(3x + 2)

Now replace the x's with (2a - b) :

3(2a - b)^2 + 17(2a - b) + 10

= (2a - b + 5)[3(2a - b) + 2]

Simplify the second term :
= (2a - b + 5)(6a - 3b + 2)

Answer 2

I would NOT recommend distributing in the 3 over the (2a - b). Instead, I see that (2a - b) appears twice in this problem, in the place you'd expect to see just a plain x.

I'd suggest temporarily removing the (2a-b) term and replacing that with x, just while you are working with the numbers. It will make it look much easier, then you can put the (2a-b) back in place of x when you finish.

3x^2 + 17x + 10
(look more familiar now?)

take the first coefficient times the last number (constant)
3(10) = 30

list factors for 30
1 and 30, 2 and 15, 3 and 10, 5 and 6

locate the pair that adds up to the middle coefficient
2 + 15 = 17

rewrite the middle term as two terms, using what you just found
3x^2 + 2x + 15x + 10

factor by grouping (first two terms, second two terms)
3x^2 + 2x factors to x(3x + 2)
15x + 10 factors to 5(3x + 2)

factor out the binomial (3x + 2)
x(3x + 2) + 5(3x + 2)
(3x + 2)(x + 5)

***you can also do the steps up to this point with other methods your teacher may have taught you, such as guess and FOIL, or using a chart or boxes. I like splitting the middle term because there is very little guesswork.


Finally, put the (2a-b) back in place of the x, now that we're pretty much done.

( 3 (2a - b) + 2 ) ( (2a - b) + 5 )

Distribute the 3 to simplify just a bit more:

(6a - 3b + 2) (2a - b + 5)

Good luck in your math classes!

Answer 3

Let 2a + b = x

Now you get the easier expression

3x^2 +17x + 10
(3x + 2)(x + 5)

plug 2a + b back in for x.

[3(2a+b) + 2](2a + b + 5)
(6a +3b + 2)(2a + b + 5)

Answer 4

Let x = 2a - b
3x² + 17x + 10
(3x + 2)(x + 5)
[3(2a - b) + 2 ][ 2a - b + 5 ]
[ 6a - 3b + 2 ] [ 2a - b + 5 ]

Answer 5

[16]
3(2a-b)^2+17(2a-b)+10
sunstituting 2a-b by x,the expression becomes
3x^2+17x+10
[Now we shall factor this expression]
=3x^2+15x+2x+10
=3x(x+5)+2(x+5)
=(x+5)(3x+2)
=(2a-b+5){3(2a-b)+2} [substituting back x by 2a-b]
=(2a-b+5)(6a-3b+2) ans

Answer 6

Uhh....take the 10..and uhhh factor the stuff from the 3(2a-b)........and then go 11km to the (MA)th+Pr(OF)
and divide by (HE)lp-1

Then the obvious answer will be is.

I+(Do+n)t NO

Answer 7

well, after u distribute and everything u would get:
12x^2 - 12xy + 34 x + 3y^2 - 17y + 10
u can factor this easily into:
(2x-y+5)(6x-3y+2)
=)