Factor this polynomial. Then select the correct factors from the options below. (You will select two factors) $$ 15 x^{3}+40 x^{2}+3 x+8 $$

Question

UpStudy AI · Accepted Answer

To factor 15x³ + 40x² + 3x + 8, we can use grouping:

1. Group the polynomial into two pairs:
  (15x³ + 40x²) + (3x + 8)

2. Factor out the common factors from each group:
  From 15x³ + 40x², factor out 5x²:
    5x²(3x + 8)
  From 3x + 8, factor out 1:
    1(3x + 8)

3. Now the polynomial becomes:
  5x²(3x + 8) + 1(3x + 8)

4. Factor out the common binomial (3x + 8):
  (3x + 8)(5x² + 1)

Thus, the factors you should select are (3x + 8) and (5x² + 1).
The factors are (3x + 8) and (5x² + 1).

Factor this polynomial. Then select the correct factors from the options below. (You will select two factors) \( 15 x^{3}+40 x^{2}+3 x+8 \)