Final Answer:
$-2h^2 - 16h + 2 + \frac{6}{h + 1}$
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Explanation:
Let’s divide $(-2h^3 - 18h^2 - 14h + 8)$ by $(h + 1)$ step by step.
Step 1: Ask — what do I multiply $h$ (from $h+1$) by to get $-2h^3$?
Answer: $-2h^2$.
Multiply $-2h^2$ by $(h + 1)$ → $-2h^3 - 2h^2$.
Subtract that from the original polynomial:
$(-2h^3 - 18h^2) - (-2h^3 - 2h^2) = -16h^2$
Bring down the next term: $-16h^2 - 14h$
Step 2: What do I multiply $h$ by to get $-16h^2$?
Answer: $-16h$.
Multiply $-16h$ by $(h + 1)$ → $-16h^2 - 16h$.
Subtract: $(-16h^2 - 14h) - (-16h^2 - 16h) = 2h$
Bring down the next term: $2h + 8$
Step 3: What do I multiply $h$ by to get $2h$?
Answer: $+2$.
Multiply $2$ by $(h + 1)$ → $2h + 2$.
Subtract: $(2h + 8) - (2h + 2) = 6$
Now we can’t divide 6 by $h$, so 6 is the remainder.
We write the answer as:
Quotient + Remainder over Divisor →
$-2h^2 - 16h + 2 + \frac{6}{h + 1}$
That’s it!
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Parent Tip: Review the logic above to help your child master the concept of division of polynomials worksheet with answer.
