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4.4E: Exercises

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    Practice Makes Perfect

    Find the Greatest Common Factor of Two or More Expressions

    In the following exercises, find the greatest common factor.

    Greatest Common Factor

    In the following exercises, find the greatest common factor.

    1. \(10p^3q,12pq^2\)
    2. \(12m^2n^3,30m^5n^3\)
    3. \(10a^3,12a^2,14a\)
    4. \(35x^3y^2,10x^4y,5x^5y^3\)
    Answer
    1. \(2pq\)
    2. \(6m^2n^3\)
    3. \(2a\)
    4. \(5x^3y\)
    Greatest Common Factor from a Polynomial

    In the following exercises, factor the greatest common factor from each polynomial.

    1. \(6m+9\)
    2. \(9n−63\)
    3. \(3x^2+6x−9\)
    4. \(8p^2+4p+2\)
    5. \(8y^3+16y^2\)
    6. \(5x^3−15x^2+20x\)
    7. \(24x^3−12x^2+15x\)
    8. \(12xy^2+18x^2y^2−30y^3\)
    9. \(20x^3y−4x^2y^2+12xy^3\)
    10. \(−2x−4\)
    11. \(−2x^3+18x^2−8x\)
    12. \(−4p^3q−12p^2q^2+16pq^2\)
    13. \(5x(x+1)+3(x+1)\)
    14. \(3b(b−2)−13(b−2)\)
    Answer
    1. \(3(2m+3)\)
    2. \(9(n−7)\)
    3. \(3(x^2+2x−3)\)
    4. \(2(4p^2+2p+1)\)
    5. \(8y^2(y+2)\)
    6. \(5x(x^2−3x+4)\)
    7. \(3x(8x^2−4x+5)\)
    8. \(6y^2(2x+3x^2−5y)\)
    9. \(4xy(5x^2−xy+3y^2)\)
    10. \(−2(x+4)\)
    11. \(−2x(x^2−9x+4)\)
    12. \(−4pq(p^2+3pq−4q)\)
    13. \((x+1)(5x+3)\)
    14. \((b−2)(3b−13)\)
    Factor by grouping

    In the following exercises, factor by grouping.

    1. \(ab+5a+3b+15\)
    2. \(8y^2+y+40y+5\)
    3. \(uv−9u+2v−18\)
    4. \(u^2−u+6u−6\)
    5. \(9p^2−15p+12p−20\)
    6. \(mn−6m−4n+24\)
    7. \(2x^2−14x−5x+35\)
    Answer
    1. \((b+5)(a+3)\)
    2. \((y+5)(8y+1)\)
    3. \((u+2)(v−9)\)
    4. \((u−1)(u+6)\)
    5. \((3p−5)(3p+4)\)
    6. \((n−6)(m−4)\)
    7. \((x−7)(2x−5)\)
    Factor by ac method
    1. \(p^2+11p+30\)
    2. \(n^2+19n+48\)
    3. \(a^2+25a+100\)
    4. \(x^2−8x+12\)
    5. \(y^2−18y+45\)
    6. \(x^2−8x+7\)
    7. \(5p−6+p^2\)
    8. \(8−6x+x^2\)
    9. \(x^2−12−11x\)
    10. \(5n^2+21n+4\)
    11. \(60y^2+290y−50\)
    Answer
    1. \((p+5)(p+6)\)
    2. \((n+3)(n+16)\)
    3. \((a+5)(a+20)\)
    4. \((x−2)(x−6)\)
    5. \((y−3)(y−15)\)
    6. \((x−1)(x−7)\)
    7. \((p−1)(p+6)\)
    8. \((x−4)(x−2)\)
    9. \((x−12)(x+1)\)
    10. \((5n+1)(n+4)\)
    11. \(10(6y−1)(y+5)\)
     
    Factor by substitution
    1. \(x^4−x^2−12\)
    2. \(x^4−3x^2−28\)
    3. \((x−3)^2−5(x−3)−36\)
    4. \(x^4−4x^2−12\)
    5. \((x+3)^2−9(x+3)−36\)
    Answer
    1. \((x^2+3)(x^2−4)\)
    2. \((x^2−7)(x^2+4)\)
    3. \((x−12)(x+1)\)
    4. \((x^2+2)(x^2−6)\)
    5. \((x−9)(x+6)\)

    This page titled 4.4E: Exercises is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Stanislav A. Trunov and Elizabeth J. Hale via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.