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)
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)
Well, well, well! It looks like we have some factoring fun to do here. Let's break down the options, shall we?
Option 1: (5−4x)(3−6x)
Hmm, multiplying these terms together wouldn't give us −24x^2+42x−15, so it's not the correct one.
Option 2: (5−4x)(6x+3)
Oh, multiplying these terms wouldn't magically transform into −24x^2+42x−15 either. So, it's not the right answer, my friend.
Option 3: (4x−5)(6x−3)
Wait a minute! This looks promising! If we expand these terms, we get 24x^2−12x−30x+15. Combining like terms, we end up with −24x^2+42x−15. Jackpot!
Option 4: (4x−5)(3−6x)
Well, well, well. This one is just a sneaky rearrangement of the previous option. So, it's also a winner!
So, my dear inquirer, the correct answer is both (3−6x)(4x−5) and (4x−5)(3−6x). They are just different orderings of the same terms. Now you have two options to impress your math pals with!
The correct answer is (4x−5)(3−6x).
To find the factored form of the expression −24x^2+42x−15, we need to find two binomials that, when multiplied together, give us the original expression.
One approach is to look for common factors that can be factored out of each term. In this case, there are no common factors among all three terms. However, we can still factor the expression by using the fact that the product of the coefficients of x^2 and the constant term must equal the product of the coefficients of x.
The coefficient of x^2 is -24, and the constant term is -15. To find two numbers whose product is -24 and whose sum is 42 (the coefficient of x), we can use trial and error or the quadratic formula.
By factoring the expression using trial and error, we can find that the expression can be factored as (4x−5)(6x−3):
(-24x^2+42x−15) = (4x−5)(6x−3)
Therefore, the correct factored form of the expression is (4x−5)(6x−3).