1. **State the problem:** Multiply the polynomials $\left(5x^2 + 2x + 8\right)\left(7x - 6\right)$. 2. **Recall the distributive property:** To multiply two polynomials, multiply each term in the first polynomial by each term in the second polynomial and then combine like terms. 3. **Multiply each term:** - $5x^2 \times 7x = 35x^3$ - $5x^2 \times (-6) = -30x^2$ - $2x \times 7x = 14x^2$ - $2x \times (-6) = -12x$ - $8 \times 7x = 56x$ - $8 \times (-6) = -48$ 4. **Combine like terms:** - Combine $-30x^2$ and $14x^2$: $$-30x^2 + 14x^2 = \cancel{-30x^2} + \cancel{14x^2} = -16x^2$$ - Combine $-12x$ and $56x$: $$-12x + 56x = \cancel{-12x} + \cancel{56x} = 44x$$ 5. **Write the final expression:** $$35x^3 - 16x^2 + 44x - 48$$ 6. **Answer choice:** This matches option C. **Final answer:** $35x^3 - 16x^2 + 44x - 48$