Joseph G. answered • 05/23/21
Graduate Student and Substitute Teacher / B.A. in Chemistry (3.85 GPA)
Firstly, 6x^2 - 9x - 15 can be factored by determining the factors of the coefficient of x^2 (the coefficient is 6) and the constant (the constant is the number without a variable, (-15)). However, I won't get into how to factor this quadratic since this is 7th grade. This will be in high school though.
Anyway, when you multiply the first side of the equation [(3x + a)(2x - 5)] you multiply each of the terms in the first parenthesis times each of the terms in the second parenthesis and add them. (You multiply the first terms in both parenthesis, plus, the first term in the first parenthesis times the second term in the second parenthesis, plus, the second term in the first parenthesis times the first term in the second parenthesis, plus, the second terms in both parenthesis multiplied together)
So for (3x + a)(2x - 5), you do 3x times 2x, plus, 3x times -5, plus, "a" times 2x, plus, "a" times -5
And you get:
6x^2 - 15x + (a)(2x) -5a
As you can see, you can determine the value of "a" immediately by realizing that if
(3x + a)(2x - 5) = 6x^2 - 9x - 15
Then -5a must equal -15 because the last term in each of the parenthesis get multiplied to determine the constant (the number without the variable)
So, knowing that -5a = -15 you can easily solve for "a"
