Which of these represents −24x2+42x−15
in factored form?
Responses
(4x−5)(6x−3)
open paren 4 x minus 5 close paren times open paren 6 x minus 3 close paren
(5−4x)(3−6x)
open paren 5 minus 4 x close paren times open paren 3 minus 6 x close paren
(5−4x)(6x+3)
open paren 5 minus 4 x close paren times open paren 6 x plus 3 close paren
(4x−5)(3−6x)
The correct answer is (4x-5)(3-6x) which, when multiplied out, gives -24x^2 + 42x - 15.
AAAaannndd the bot gets it wrong yet again!
-24x2+42x-15 = -3(2x-1)(4x-5)
The correct answer is (4x−5)(3−6x).
To determine the factored form of the quadratic equation −24x^2 + 42x − 15, we need to find the two binomials that multiply together to give us the original equation.
First, let's find the factors of the coefficient of x^2, which is -24. The possible factor pairs of -24 are:
(-24, 1), (-12, 2), (-8, 3), (-6, 4)
Next, let's find the factors of the constant term, -15. The possible factor pairs of -15 are:
(-15, 1), (-5, 3)
Our goal is to find the combination of these factors that gives us the middle term coefficient, which is 42x.
Let's try the first factor pairs: (-24, 1) and (-15, 1).
Multiplying them together, we get (-24)(-15) = 360. It doesn't give us the desired middle term coefficient of 42x.
Let's try the next factor pairs: (-12, 2) and (-15, 1).
Multiplying them together, we get (-12)(-15) = 180. It also doesn't give us the desired middle term coefficient of 42x.
Let's try the next factor pairs: (-8, 3) and (-15, 1).
Multiplying them together, we get (-8)(-15) = 120. Again, it doesn't give us the desired middle term coefficient of 42x.
Finally, let's try the last factor pairs: (-6, 4) and (-5, 3).
Multiplying them together, we get (-6)(-5) = 30. This time, it does give us the desired middle term coefficient of 42x.
So, the factored form of the quadratic equation −24x^2 + 42x − 15 is (4x−5)(3−6x).