High School Math : Simplifying Polynomial Functions

Study concepts, example questions & explanations for High School Math

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Example Questions

Example Question #15 : Pre Calculus

Simplify the following polynomial:

\(\displaystyle (\frac{-a^{-2}b^{3}c^{-1}}{3a^{-4}b^{-1}c^{3}})^{-2}\)

Possible Answers:

\(\displaystyle \frac{9a^{4}}{c^{8}b^{4}}\)

\(\displaystyle \frac{9c^{8}}{a^{4}b^{8}}\)

\(\displaystyle \frac{9b^{8}}{c^{8}a^{4}}\)

\(\displaystyle \frac{9a^{4}}{c^{8}b^{8}}\)

\(\displaystyle \frac{c^{8}}{9a^{4}b^{8}}\)

Correct answer:

\(\displaystyle \frac{9c^{8}}{a^{4}b^{8}}\)

Explanation:

To simplify the polynomial, begin by combining like terms:

\(\displaystyle (\frac{-a^{-2}b^{3}c^{-1}}{3a^{-4}b^{-1}c^{3}})^{-2}\)

\(\displaystyle (\frac{-a^{2}b^{4}}{3c^{4}})^{-2}\)

Example Question #21 : Pre Calculus

Simplify the following polynomial function:

\(\displaystyle ab^{-2}(a^{2}b + a^{-1}b^{3}-a^{3}b^{-1})\)

Possible Answers:

\(\displaystyle \frac{a^{3}}{b}-b+\frac{a^{4}}{b^{3}}\)

\(\displaystyle \frac{a^{3}}{b}-\frac{a^{4}}{b^{3}}\)

\(\displaystyle \frac{a^{3}}{b}+b^{2}-\frac{a^{4}}{b^{3}}\)

\(\displaystyle \frac{a^{3}}{b}+b-\frac{a^{4}}{b^{3}}\)

\(\displaystyle \frac{a^{3}}{b}+\frac{a^{4}}{b^{3}}\)

Correct answer:

\(\displaystyle \frac{a^{3}}{b}+b-\frac{a^{4}}{b^{3}}\)

Explanation:

First, multiply the outside term with each term within the parentheses:

\(\displaystyle ab^{-2}(a^{2}b + a^{-1}b^{3}-a^{3}b^{-1})\)

\(\displaystyle a^{3}b^{-1} + b-a^{4}b^{-3}\)

Rearranging the polynomial into fractional form, we get:

\(\displaystyle \frac{a^{3}}{b}+b-\frac{a^{4}}{b^{3}}\)

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