Answer:
To factor the polynomial 40x^3 + 70x^2 + 30x, we can first factor out the greatest common factor of the terms, which is 10x:
10x(4x^2 + 7x + 3)
Next, we can factor the quadratic expression inside the parentheses. We need to find two numbers that multiply to give 4 × 3 = 12 and add to give 7. These numbers are 4 and 3:
10x(4x + 3)(x + 1)
Therefore, the factored form of the polynomial is:
10x(4x + 3)(x + 1)