Subtract the polynomials. SHOW ALL WORK for full credit. (4x^2-2x+3)-(-2x^2+6x-3) Find the product. Show all work. (x-3)(4x^2-2x+3)

To subtract the polynomials, we need to distribute the negative sign to each term in the second polynomial and then combine like terms.<br /><br />$(4x^{2}-2x+3)-(-2x^{2}+6x-3)$<br /><br />Distribute the negative sign:<br />$(4x^{2}-2x+3) + (2x^{2}-6x+3)$<br /><br />Combine like terms:<br />$(4x^{2} + 2x^{2}) + (-2x - 6x) + (3 + 3)$<br />$= 6x^{2} - 8x + 6$<br /><br />Therefore, the result of subtracting the polynomials is $6x^{2} - 8x + 6$.<br /><br />To find the product of $(x-3)(4x^{2}-2x+3)$, we need to use the distributive property and multiply each term in the first polynomial by each term in the second polynomial.<br /><br />$(x-3)(4x^{2}-2x+3)$<br /><br />Multiply each term in the first polynomial by each term in the second polynomial:<br />$x(4x^{2}) + x(-2x) + x(3) - 3(4x^{2}) - 3(-2x) - 3(3)$<br /><br />Simplify:<br />$4x^{3} - 2x^{2} + 3x - 12x^{2} + 6x - 9$<br /><br />Combine like terms:<br />$4x^{3} - 14x^{2} + 9x - 9$<br /><br />Therefore, the product of $(x-3)(4x^{2}-2x+3)$ is $4x^{3} - 14x^{2} + 9x - 9$.