Could you help me to factorise the following 3x squared - 2x - 5, 8a squared + 10a - 3, 10x squared + 19x + 7

Question

Could you help me to factorise the following:
3x squared - 2x - 5
8a squared + 10a - 3
10x squared + 19x + 7
15a squared - 14a - 8
12a squared - 20a + 3
12a squared + 11a - 15
Can you tell me step by step explanations as you go

Answer 1

1. (3x-5)(x+1)
2. (4a-1)(2a+3)
3. (5x+7)(2x+1)
4. (3a+4)(5a-2)
5. (2a-3)(6a-1)
6. (4a-3)(3a+5)

Answer 2

Follow these steps:

1: ( ) ( )
2: Now you have to remember FOIL. So start with factors of the squared (first) term
3: (3x ) (x )
4: Now the trick is to factor the last term so that when you do the "outside" and "inside" part of foil that they will come out to 2(for the 2x)
5: (3x 1) (x 5) will not work because when you multiply 5 time 3 and 1 time 1 you get 15 and 1 and there is no way to make them add up to 2.
6: However if you do (3x 5) (x 1) then you will multiply 1 by 3 and 5 by 1 and if you subtract 3 from 5 then you get 2. So this is the correct numerical configuration
7: Now you have to determine what signs to use. The negative sign next to the 5 tells you that the signs will be different. The negative sign next to the 2 tells you that the bigger multipled pair (in this case 1 and 5) will have the negative sign associated with it.
8 therefore you get (3x-5)(x+1)

Work through the same process on the other two.

Answer 3

Different people do it different ways....I use something called "decomposition"....it comes in really handy for these kinds of equations.

I'll do 12a^2 - 20a + 3 as an example.

1. Take the first and the last terms and multiply them.

12 * 3 = 36

2. Find two different numbers which when multiplied, yield a product of 36, but when added yield a sum of -20 (yes, always look at the sign in front)

18 * 2 = 36

-18*-2= 36 -18+ -2 = -20

3. Replace the middle term in the quadratic equation with your chosen numbers.

12a^2 -18a -2a+3

4. Treat each side of this "expanded" equation separately, and factor.

12a^2 -18a -2a+3
6a(2a-3) -1(2a-3)--->because -(-) = +

5. Combine ( ) ( ) both factored sides. One factor should be repeated on both...if not go back and check your signs and your factoring!

(6a-1)(2a-3)<--the repeated one is only written once in the final form.

6. FOIL your answer to check.

12a^2 -18a - 2a +3

= 12a^2 -20a + 3

COOL! :)

* This method seems to have more steps involved and may be more time-consuming, but practice it lots following every step, and you'll never go wrong.

It's important that you get good at factoring because you'll be needing it for any higher-level math courses you may need to take in future...like it or not. I've had to keep at it from grade 10 to first-year Calculus in university....yeah...learn it well...at least until grade 11, trust me!

Answer 4

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


8a^2+10a-3
(4a-1)(2a+3)

10x^2+19x+7
(5x+7)(2x+1)

15a^2 - 14a - 8
(5a+2)(3a-4)

12a^2 - 20a + 3
(6a-1)(2a-3)

12a^2 + 11a - 15
(4a-3)(3a+5)


Explanation: I just stare them into sunmission.