6.11: Proficiency Exam

Elementary Algebra · LibreTexts

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    From LibreTexts, under CC BY 4.0, as the source states it; its equations are written in TeX, which the PDF shows typeset. This page at LibreTexts.

    Exercise \(\PageIndex{1}\)

    The product is \(27a^3+9a^2+9a\) and a factor is \(3a\). Find the other factor.

    Answer

    \(9a^2+3a+3\)

    Exercise \(\PageIndex{2}\)

    The product is \(15x^{n+5}y^{3n−2}\). Find the other factor.

    Answer

    \(5x^ny^{2n−3}\)

    For the following problems, factor, if possible, the polynomials.

    Exercise \(\PageIndex{3}\)

    \(−14x^2y^4b−28x^2y^3b−42x^2y^2\)

    Answer

    \(−14x^2y^2(y^2b+2yb+3)\)

    Exercise \(\PageIndex{4}\)

    \((y+2)a+(y+2)c\)

    Answer

    \((a+c)(y+2)\)

    Exercise \(\PageIndex{5}\)

    \( 6x^2y^2z+5x^2y^3−12xyz−10xy^2\)

    Answer

    \(xy(xy−2)(6z+5y)\)

    Exercise \(\PageIndex{6}\)

    \(4a^2−16c^2\)

    Answer

    \(4(a+2c)(a−2c)\)

    Exercise \(\PageIndex{7}\)

    \(m^4−n^4\)

    Answer

    \((m^2+n^2)(m+n)(m−n)\)

    Exercise \(\PageIndex{8}\)

    \(b^2+8b+16\)

    Answer

    \((b+4)^2\)

    Exercise \(\PageIndex{9}\)

    \(9y^2−30y+25\)

    Answer

    \((3y−5)^2\)

    Exercise \(\PageIndex{10}\)

    \(x^2+5x−15\)

    Answer

    not factorable

    Exercise \(\PageIndex{11}\)

    \(x^2−x−30\)

    Answer

    \((x−6)(x+5)\)

    Exercise \(\PageIndex{12}\)

    \(4x^6−36x^4+80x^2\)

    Answer

    \(4x^2(x^2−5)(x+2)(x−2)\)

    Exercise \(\PageIndex{13}\)

    \(9x^2+25x−6\)

    Answer

    \((9x−2)(x+3)\)

    This page titled 6.11: Proficiency Exam was last modified on Sun, 04 Jun 2023 00:34:01 GMT and is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Denny Burzynski and Wade Ellis, Jr. (OpenStax CNX) .