Final answer:
To find the product of (4x+3) and (2x²–5x – 3), use the distributive property to multiply each term and then combine like terms.
Step-by-step explanation:
To find the product of the binomial (4x+3) with the trinomial (2x²–5x – 3), we can use the distributive property. We will multiply each term in the binomial by each term in the trinomial and then combine like terms.
First, we multiply the first term of the binomial, 4x, by each term in the trinomial: 4x * 2x² = 8x³, 4x * -5x = -20x², and 4x * -3 = -12x.
Next, we multiply the second term of the binomial, 3, by each term in the trinomial: 3 * 2x² = 6x², 3 * -5x = -15x, and 3 * -3 = -9.
Finally, we combine like terms: (8x³ - 20x² - 12x) + (6x² - 15x - 9) = 8x³ + 6x² - 20x² - 12x - 15x - 9 = 8x³ - 14x² - 27x - 9.