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Algebra 1 (Eureka Math/EngageNY)

Sal factors 4y^2+4y-15 as (2y-3)(2y+5) by grouping. Created by Sal Khan and Monterey Institute for Technology and Education.

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• i really can not bare the curiosity of why the tecnic Sal uses(in problem 4y^+4y-15,
a+b=4*15)makes sense. why do you have to multiply the product of y^ and 15?
i get that if you multiply that way you can solve the problems but i'm pretty sure that the mathmetician who dicovered this didn't figure out is suddenly with no thought.
i know it works but can someone please tell me WHY it works?
(1 vote)
• Any equation with a factored form of (ax+b)(cx+d) will multiply, by distribution, to get acx^2 + (ad + bc)x + bd.

You can then multiply the coefficient of x^2 and the constant (ac*bd) like the instructor suggests.

Notice that this is all multiplication a*c*b*d, therefore, using the commutative property, ac*bd=ad*bc.

ad*bc is the product of the two numbers, ad and bc, who's sum is the middle term of the trinomial.
• Can somebody tell me why grouping works? I get that it's factoring, but how do we know to split the middle number into factors of the multiple of the first coefficient and the last constant? Are there any videos or links explaining this?
• When a number is written such that,
(a+x)(b+x)
It can also be factorize as
ab+ax+xb+x^2
as we factorize it we get first factor as ab
and the 2nd and 3rd factor as ax+bx.
So we're kinda just doing the reverse of it for quadratic polynomial like these by finding two number which satisfy both ab and ax+bx.
Hope it helps :D
• Do you have any tutorial videos on factoring by GCF?
• Yes he does, it starts with Factoring and the Distributive Properties, and then he does two more videos to hit the point home, in Factoring and the Distributive Properties 2, and Factoring and the Distributive Properties 3. Enjoy and have fun with it!
• I still don't get where the minus 60 is coming from...
• What would you do if it was a positive 15 instead of a negative 15?
• no, that equals 4y^2 + 16y + 15

You can not factor that except for taking a 4 out of it. If you try to solve for the zeros you cant do that either. You end up with a negative square root in the quadratic equation.
• How do you continue factoring this: 2x(x+4)+5(x+2)
• The quadratic formula or completing square after expansion
(1 vote)
• for the 4 * 15, is it the A term 4, or the B term 4
• so at the part where he had the 2 factors -6 and 10 how did you know which factor to put down first
• The order doesn't matter. The only thing thatt matters is that the 2 terms need to add back to the original value (in this case 4y). I'll reverse the 2 terms and redo the problem in the video so that you can see.
4y^2 + 10y - 6y - 15
2y (2y + 5) - 3 (2y + 5)
(2y + 5)(2y - 3)
These are the same 2 factors that Sal created in the video.
Hope this helps.