I've always been horrible when it comes to numbers. I even go to tutoring and I still don't get the following problems. These are math questions on a test that I got wrong. I will provide the solutions and the questions. All I need is an explanation on how to get to the solutions. Any assistance will be greatly appreciated. All the questions require me to factor them by the way.
1) 6- 19u+ 10u^2 Solution: (2u-3) (5u-2)
2) 15x^2 - 10x + 25 Solution: 5(3x-5) (x+1)
3) 14b^2 + 29b + 12 Solution: (2b+3) (7b+4)
4) 12y^2 + 11y + 2 Solution: (3y+2) (4y+1)
1) 6- 19u+ 10u^2 Solution: (2u-3) (5u-2)
2) 15x^2 - 10x + 25 Solution: 5(3x-5) (x+1)
3) 14b^2 + 29b + 12 Solution: (2b+3) (7b+4)
4) 12y^2 + 11y + 2 Solution: (3y+2) (4y+1)
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1) FOIL first outer inner last
For convenience, rewrite as: 10u^2 - 19u + 6
(2u - 3) (5u - 2)
Multiply first terms 2u*5u = 10u^2
Multiply outer terms -2 * 2u = -4u
multiply inner terms -3 * 5u = -15 u
To get middle term, add the previous 2 (inner/outer)...thats -19u
Multiply last terms.... -3 * -2 = 6
So, 10u^2 - 19u + 6
The remaining 3 are also FOIL. In number 2 a common factor of 5 is factored out in advance of the FOIL. Basically...with foil..you just look for factors of the numbers that will match up with your desired terms.
For convenience, rewrite as: 10u^2 - 19u + 6
(2u - 3) (5u - 2)
Multiply first terms 2u*5u = 10u^2
Multiply outer terms -2 * 2u = -4u
multiply inner terms -3 * 5u = -15 u
To get middle term, add the previous 2 (inner/outer)...thats -19u
Multiply last terms.... -3 * -2 = 6
So, 10u^2 - 19u + 6
The remaining 3 are also FOIL. In number 2 a common factor of 5 is factored out in advance of the FOIL. Basically...with foil..you just look for factors of the numbers that will match up with your desired terms.