1. **State the problem:** Factor the polynomial $$4x^3 - x^2 + 8x - 2$$ by grouping. 2. **Group terms:** Group the polynomial into two pairs: $$ (4x^3 - x^2) + (8x - 2) $$ 3. **Factor out the greatest common factor (GCF) from each group:** - From $$4x^3 - x^2$$, the GCF is $$x^2$$, so factor it out: $$ x^2(4x - 1) $$ - From $$8x - 2$$, the GCF is $$2$$, so factor it out: $$ 2(4x - 1) $$ 4. **Rewrite the expression:** $$ x^2(4x - 1) + 2(4x - 1) $$ 5. **Factor out the common binomial factor:** $$ (4x - 1)(x^2 + 2) $$ 6. **Final answer:** $$4x^3 - x^2 + 8x - 2 = (4x - 1)(x^2 + 2)$$ This shows the polynomial is factorable by grouping, and the factored form is $$ (4x - 1)(x^2 + 2) $$.