Section 1.6P: Practice

MTH 65: Algebra 2 · LibreTexts

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    Practice Makes Progress

    In the following exercises, divide each polynomial by the monomial.

    Exercise

    \(\dfrac{30b+75}{5}\)

    Exercise

    \((55w^2−10w)÷5w\)

    Exercise

    \(\dfrac{72r^{5}s^2+132r^{4}s^3−96r^{3}s^5}{12r^{2}s^2}\)

    Exercise

    \(\dfrac{63a^3−108a^2+99a}{9a^2}\)

    In the following exercises, divide each polynomial by the binomial.

    Exercise

    \((x^2−14x+49)÷(x−7)\)

    Exercise

    \((4x^2−17x−15)÷(x−5)\)

    Exercise

    \((x^2+2x−30)÷(x−5)\)

    Exercise

    \((2n^3−10n+28)÷(n+3)\)

    Exercise

    \((m^3+1000)÷(m+10)\)

    Exercise

    \((x^3−216)÷(x−6)\)

    Everyday Math

    Exercise

    At a company meeting, every employee shakes hands with every other employee. The number of handshakes is given by the expression \(\dfrac{n^2−n}{2}\) where \(n\) represents the number of employees. How many handshakes will there be if there are 10 employees at the meeting?

    Writing Exercises

    Exercise

    Divide \(\dfrac{10x^2+x−12}{2x}\) and explain with words how you get each term of the quotient.

    Self Check

    Use this checklist to evaluate your mastery of the objectives of this section.

    This is a table that has three rows and four columns. In the first row, which is a header row, the cells read from left to right “I can…,” “Confidently,” “With some help,” and “No-I don’t get it!” The first column below “I can…” reads “divide a polynomial by a monomial,” and “divide a polynomial by a binomial.” The rest of the cells are blank.

    If most of your checks were:

    …confidently. Congratulations! You have achieved the objectives in this section. Reflect on the study skills you used so that you can continue to use them.

    …with some help. This must be addressed quickly because topics you do not master become potholes in your road to success. In math, every topic builds upon previous work. It is crucial to establish a strong foundation before proceeding. Who can you ask for help? Your classmates, tutors, and class instructor are good resources.

    …no - I don’t get it! This is a warning sign, and you must not ignore it. You should get help right away, or you will quickly be overwhelmed. Meet with your instructor during their drop-in hours as soon as you can to discuss your situation. Together, you can devise a plan to get the help you need.

    This page titled Section 1.6P: Practice was last modified on Wed, 27 Aug 2025 20:41:47 GMT and is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Math Department via source content that was edited to the style and standards of the LibreTexts platform.