Question

3, x, cubed, plus, 8, x, squared, plus, 8, x, plus, 53x
3
+8x
2
+8x+5 is divided by 3, x, plus, 53x+5.

Answer 1

Interpreting the divisor as 3x + 5, divide 3x^3 + 8x^2 + 8x + 5 by 3x + 5.

Long division:
- (3x^3)/(3x) = x^2 → x^2(3x+5) = 3x^3 + 5x^2. Subtract → 3x^2 + 8x.
- (3x^2)/(3x) = x → x(3x+5) = 3x^2 + 5x. Subtract → 3x + 5.
- (3x)/(3x) = 1 → 1·(3x+5) = 3x + 5. Subtract → 0.

Quotient = x^2 + x + 1, remainder = 0. So
3x^3 + 8x^2 + 8x + 5 = (3x + 5)(x^2 + x + 1).