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## Algebra 1 (Eureka Math/EngageNY)

Sal solves the equation s^2-2s-35=0 by factoring the expression on the left as (s+5)(s-7) and finding the s-values that make each factor equal to zero. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• How would you work out the problem 9k^2 + 45k = 0
• factor out 9k from the expression u get: 9k(k+5)= 0, which means 9k = 0, k + 5 = 0, solving for k you get: k = 0, k = -5
• What would happen if the starting equation didn't equal up to zero, how would you factor those types of problems?
• great question. Let's use the equation 3s^2 + 6 + 1 = -1. With this you combine like terms so you would add 1 to the -1 to get the equation to equal 0. Because t is compatible with our 1 in the equation you would combine them because they are like terms. You then solve the equation like Sal explains.
• How would you factor this?
2x^2+5x-3

It would be (2x-1)(x+3)
3 is a prime number.. so the only two numbers that can be multiplied to get 3 are 3 and 1. Those two numbers do not add up to 5. How could you solve the part for 5x?
• Good question!
Actually, when we are solving these types of problems, we want to take the product of the coefficient of x^2 and the constant term. In this case that would be nothing but -6.
-6 can be written as the product of 6 and -1.
So, the equation would become
2x^2 + 5x -3 = 2x^2 + 6x - x -3
= 2x(x + 3) - (x + 3)
Now, factoring out the (x + 3), the equation becomes:
=> (x + 3)(2x - 1)
Hope this helped!
• (x - 2) (x + 4) = 0
• To solve this, you would use the zero product property. If you make one of the parentheses equal to zero then the whole left side is equal to zero (because zero multiplied by anything is zero). So you'd set the first set of parentheses like so: (x-2)=0. Then to isolate "x", you would add 2 to both sides to get x=2. Then, You would set the other set of parentheses to zero, like so: (x+4)=0. To isolate "x", you would subtract 4 from both sides to get x=-4. So, your final answer would be x=2 or x=-4.

Hope this helped you out.
• At why does he do A + B = -2?
• It's the formula for finding the solutions to the quadratic.
What he is saying is you need 2 numbers that when added together equal -2, but when multiplied equals -35.
Note: since the multiplied is negative, one of the two numbers will be negative and the other will be positive.
• I'm pretty confused about this; I wasn't following my teacher when she went over it. So how do I solve (I need to factor it) a problem like this:
5x^2 + 17x - 12
• I've learned this in a mathsmart book that you can buy from costco. What you do is you multiply a and c together (5x^2*-12) and you get -60x^2. Find two numbers that add up to 17x and multiply to -60x^2, those numbers would turn out to be 20x and -3x. Now you write in the equation 5x^2+20x-3x-12 = 5x(x+4)+-3(x+4) = (5x-3)(x+4)
• It's really never a good idea to use s and 5 together. I don't even have dyslexia but when I'm learning something you should try to use numbers and variables that don't look similar cause its hard to view.
• I actually can't even tell the difference between his s and 5
• At , I don't clearly understand how Sal factors out the

( s + 5 ) in the expression s( s + 5 ) - 7 ( s + 5 ) into ( s + 5 )( s - 7 ). How does he do it?
• Sal used the distribution property, if you had A*B - C*B you can change this to B(A-C).
`A * B - C * B = B * (A-C)So s * ( s + 5 ) - 7 * ( s + 5 ) = ( s + 5 ) * ( s - 7 ).`