express the product of 2x^2 + 6x-8 and x+3 in standard form.
To find the product of two polynomials, we can use the distributive property to multiply each term in the first polynomial by each term in the second polynomial, and then combine like terms.
Let's multiply term by term:
(2x^2 + 6x - 8) * (x + 3)
= (2x^2 * x) + (2x^2 * 3) + (6x * x) + (6x * 3) + (-8 * x) + (-8 * 3)
= 2x^3 + 6x^2 + 6x^2 + 18x - 8x - 24
Now, let's combine like terms:
= 2x^3 + (6x^2 + 6x^2) + (18x - 8x) - 24
= 2x^3 + 12x^2 + 10x - 24
So, the product of 2x^2 + 6x - 8 and x + 3 in standard form is 2x^3 + 12x^2 + 10x - 24.