Checkpoint: Polynomial Long Division with Remainders Solution

Simplify.
$(3 p^{3} - 8 p + 14) \div (p - 6)$

$p - 6 3 p^{2} + 18 p + 100 3 p^{3} + 0 p^{2} - 8 p + 14 - (3 p^{3} - 18 p^{2}) 18 p^{2} - 8 p - (18 p^{2} - 108 p) 100 p + 14 - (100 p - 600) 614 + \frac{614}{p - 6}$

$(p - 6) (3 p^{2} + 18 p + 100) + 614 3 p^{3} + 18 p^{2} + 100 p - 18 p^{2} - 108 p - 600 + 614 3 p^{3} - 8 p + 14 ✓$

Note

Q: What is the divisor for the problem?
A: (p − 6)

Q: What can be used to show division other than a division symbol?
A: Raising the divisor to the negative first power.

Q: Is the divisor a factor of the polynomial? Explain.
A: No, because there is a remainder with dividing.