1Cademy - Finding the Quotient $$(-48a^8b^4 - 36a^6b^5) \div (-6a^3b^3)$$

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Dividing a Polynomial by a Monomial

Example

Finding the Quotient $(-48a^8b^4 - 36a^6b^5) \div (-6a^3b^3)$

Divide a two-variable binomial with higher-degree terms by a negative two-variable monomial: $(-48a^8b^4 - 36a^6b^5) \div (-6a^3b^3)$ .

Step 1 — Rewrite as a fraction. Set up the problem with the polynomial over the monomial: $\frac{-48a^8b^4 - 36a^6b^5}{-6a^3b^3}$ .

Step 2 — Separate the terms. Rewrite the expression as the difference of two separate fractions: $\frac{-48a^8b^4}{-6a^3b^3} - \frac{36a^6b^5}{-6a^3b^3}$ .

Step 3 — Simplify each fraction. For the first fraction: dividing a negative by a negative yields a positive, so $\frac{-48}{-6} = 8$ . Subtracting the exponents gives $\frac{a^8}{a^3} = a^{8-3} = a^5$ and $\frac{b^4}{b^3} = b^{4-3} = b$ . The simplified term is $8a^5b$ . For the second fraction: dividing a positive by a negative yields a negative, so $\frac{36}{-6} = -6$ . Subtracting the exponents gives $\frac{a^6}{a^3} = a^{6-3} = a^3$ and $\frac{b^5}{b^3} = b^{5-3} = b^2$ . The simplified term is $-6a^3b^2$ . The expression is subtracting this term, so it becomes $-(-6a^3b^2)$ , which is $+6a^3b^2$ .

The quotient is $8a^5b + 6a^3b^2$ .

Updated 2026-04-29

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OpenStax Intermediate Algebra

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