29 $$ 6 x^{3}-48 x^{2}+5 x-40 $$

Question

UpStudy AI · Accepted Answer

1. Write the polynomial:
   
   $$
   6x^3 - 48x^2 + 5x - 40
   $$

2. Group the terms:

$$
   \left(6x^3 - 48x^2\right) + \left(5x - 40\right)
   $$

3. Factor out the common factor from each group:

- From the first group, factor out $$6x^2$$:

$$
     6x^3 - 48x^2 = 6x^2(x - 8)
     $$

- From the second group, factor out $$5$$:

$$
     5x - 40 = 5(x - 8)
     $$

4. Notice the common factor $$(x - 8)$$ in both groups. Factor it out:

$$
   6x^3-48x^2+5x-40 = (x-8)\left(6x^2+5\right)
   $$

5. The fully factored form of the polynomial is:

$$
   (x-8)(6x^2+5)
   $$
The polynomial $$6x^3 - 48x^2 + 5x - 40$$ can be factored as $$(x - 8)(6x^2 + 5)$$.

29 \( 6 x^{3}-48 x^{2}+5 x-40 \)