Question

factor the polynomial completely and SHOW WORK i’ve been on it for the past 30 minutes and I want to cry 24x^3-78x^2+45x NO LINKS pls :))

Answer 1

9514 1404 393

Answer:

  3(x)(4x -3)(2x -5)

Step-by-step explanation:

First of all, recognize that all coefficients are multiples of 3, and all terms have x as a common factor. This means your first factorization is ...

  (3x)(8x^2 -26x +15)

Now, you can use the "X-method" or similar to factor the quadratic. Start by looking for factors of (8)(15) = 120 that have a total of -26. Both will be negative. Here is a list of the positive factor pairs.

  120 = 1·120 = 2·60 = 3·40 = 4·30 = 5·24 = 6·20 = 8·15 = 10·12

The sums of these factor pairs are ...

  121, 62, 43, 34, 29, 26, 23, 22

The pair with a sum of 26 is highlighted.

Using this information, you can complete the X-method diagram, or you can use these numbers to rewrite the quadratic x-term to have 2 parts:

  8x^2 -20x -6x +15

Now, the quadratic can be factored by grouping:

  =  (8x^2 -20x) +(-6x +15)

  = 4x(2x -5) +3(-2x +5)

Recognizing the sign difference between the parentheses contents, we can factor the quadratic to be ...

  = (4x -3)(2x -5) . . . . . note the sign gets attached to the 3

So, the complete factorization of the original expression is ...

  24x^3-78x^2+45x = 3(x)(4x -3)(2x -5)