Which of these represents −24x2+42x−15

in factored form?
Responses

(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)(6x−3)
open paren 4 x minus 5 close paren times open paren 6 x minus 3 close paren

(4x−5)(3−6x)

1 answer

The correct answer is (4x-5)(3-6x).

To factor the expression, we need to find two numbers that multiply to give -24 and add to give 42. These numbers are -3 and 8.

Then, we can write the expression as:

-24x^2 + 42x - 15 = -3(8x^2 - 14x + 5)

Next, we can factor the quadratic expression inside the parentheses:

8x^2 - 14x + 5 = (4x - 5)(2x - 1)

Substituting this back into the original expression, we get:

-24x^2 + 42x - 15 = -3(4x - 5)(2x - 1)

Finally, we can simplify this expression by distributing the -3:

-24x^2 + 42x - 15 = (4x - 5)(-6x + 3) = (4x - 5)(3 - 6x)