Answer: To find the remainder when 4x^3 - 8x^2 + 3x - 7 is divided by 4x - 3, we can use polynomial long division.
Here's how:
4x^3 - 8x^2 + 3x - 7
÷ 4x - 3
4x^2
4x^2
______
0x^3 + 4x^2 - 8x^2 + 3x - 7
-4x^2 -12x^2
-12x^2
-12x^2
________
0x^2 - 8x^2 + 3x - 7
+12x^2 -36x^2
-24x^2
-24x^2
________
-24x^2 + 3x - 7
+24x^2 +72x^2
48x^2
48x^2
________
48x^2 - 3x + 1
-48x^2 +144x^2
192x^2
________
192x^2 + 1
The remainder is 192x^2 + 1.
Explanation: