The problem
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Can you explain the first step in factoring this problem?
9x^2+3x-20
9x^2-12x+15x-20
How were -12 and 15 chosen to be factors
Answer provided by our tutors
If you solve the quadratic equation
9x^2+3x-20=0
You will see that the solutions are:
x1 = 4/3
x2 = - 5/3
Since we know the solutions, we know that (x - 4/3) and (x-(-5/3)) are factors of 9x^2+3x-20, that is:
9x^2+3x-20 = 9*(x - 4/3)(x - (-5/3))
9*(x - 4/3)(x - (-5/3)) = 3*(x - 4/3)3*(x + 5/3)= (3x - 4)(3x + 5) = 9x^2 - 12x + 15x - 20