21) $$ 35 x^{3}-28 x^{2}-20 x+10 $$

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It seems that the expression $$ 35 x^{3}-28 x^{2}-20 x+10 $$ is not easily factored using the available tools. However, we can try to factor it manually.

1. **Factor out the greatest common factor (GCF)**:
   The GCF of the coefficients $$ 35, -28, -20, 10 $$ is $$ 1 $$ (since they do not share a common factor greater than 1). However, we can factor out $$ 5 $$ from the entire expression:

$$
   35 x^{3}-28 x^{2}-20 x+10 = 5(7 x^{3}-4 x^{2}-4 x+2)
   $$

2. **Attempt to factor the cubic polynomial $$ 7 x^{3}-4 x^{2}-4 x+2 $$**:
   We can use the Rational Root Theorem to test for possible rational roots. The possible rational roots are the factors of the constant term $$ 2 $$ divided by the factors of the leading coefficient $$ 7 $$. The possible rational roots are $$ \pm 1, \pm 2, \pm \frac{1}{7}, \pm \frac{2}{7} $$.

3. **Testing possible roots**:
   Let's test $$ x = 1 $$:

$$
   7(1)^{3} - 4(1)^{2} - 4(1) + 2 = 7 - 4 - 4 + 2 = 1 \quad (\text{not a root})
   $$

Now, let's test $$ x = -1 $$:

$$
   7(-1)^{3} - 4(-1)^{2} - 4(-1) + 2 = -7 - 4 + 4 + 2 = -5 \quad (\text{not a root})
   $$

Next, let's test $$ x = 2 $$:

$$
   7(2)^{3} - 4(2)^{2} - 4(2) + 2 = 56 - 16 - 8 + 2 = 34 \quad (\text{not a root})
   $$

Finally, let's test $$ x = \frac{1}{7} $$:

$$
   7\left(\frac{1}{7}\right)^{3} - 4\left(\frac{1}{7}\right)^{2} - 4\left(\frac{1}{7}\right) + 2 = \frac{7}{343} - \frac{4}{49} - \frac{4}{7} + 2
   $$

This calculation is complex, and it seems that the cubic polynomial does not have simple rational roots.

4. **Conclusion**:
   The expression $$ 35 x^{3}-28 x^{2}-20 x+10 $$ can be factored as:

$$
   5(7 x^{3}-4 x^{2}-4 x+2)
   $$

However, the cubic polynomial $$ 7 x^{3}-4 x^{2}-4 x+2 $$ does not factor nicely into simpler polynomials with rational coefficients. Further numerical methods or graphing may be required to find approximate roots or to analyze the polynomial further.
The expression $$ 35 x^{3}-28 x^{2}-20 x+10 $$ can be factored as $$ 5(7 x^{3}-4 x^{2}-4 x+2) $$. The cubic polynomial $$ 7 x^{3}-4 x^{2}-4 x+2 $$ does not factor nicely with rational coefficients.

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