Answer Key 10.8

  1. x=5, x=2
    x-5=0, x-2=0

    0=(x-5)(x-2)
    0=x^2-7x+10

  2. x=3, x=6
    x-3=0, x-6=0

    (x-3)(x-6)=0
    0=x^2-9x+18

  3. x=20, x=2
    x-20=0, x-2=0

    0=(x-20)(x-2)
    0=x^2-22x+40

  4. x=13, x=1
    x-13=0, x-1=0

    0=(x-13)(x-1)
    0=x^2-14x+13

  5. x=4, x=4
    x-4=0, x-4=0

    0=(x-4)(x-4)
    0=x^2-8x+16

  6. x=0, x=9
    x-9=0, x

    x(x-9)=0
    0=x^2-9x

  7. x=\dfrac{3}{4}, x=\dfrac{1}{4} \\
    x-\dfrac{3}{4}=0, x-\dfrac{1}{4}=0

    0=\left(x-\dfrac{3}{4}\right)\left(x-\dfrac{1}{4}\right) \\
    0=x^2-x+\dfrac{3}{16}

  8. x=\dfrac{5}{8}, x=\dfrac{5}{7} \\
    x-\dfrac{5}{8}=0, x-\dfrac{5}{7}=0

    0=\left(x-\dfrac{5}{8}\right)\left(x-\dfrac{5}{7}\right) \\
    0=x^2-\dfrac{75}{56}x+\dfrac{25}{56}

  9. x=\dfrac{1}{2}, x=\dfrac{1}{3} \\
    x-\dfrac{1}{2}=0, x-\dfrac{1}{3}=0

    0=\left(x-\dfrac{1}{2}\right)\left(x-\dfrac{1}{3}\right) \\
    0=x^2-\dfrac{5}{6}x+\dfrac{1}{6}

  10. x=\dfrac{1}{2}, x=\dfrac{2}{3} \\
    x-\dfrac{1}{2}=0, x-\dfrac{2}{3}=0

    0=\left(x-\dfrac{1}{2}\right)\left(x-\dfrac{2}{3}\right) \\
    0=x^2-\dfrac{7}{6}x+\dfrac{1}{3}

  11. x=5, x=-5
    x-5=0, x+5=0

    0=(x-5)(x+5)
    0=x^2-25

  12. x=1, x=-1
    x-1=0, x+1=0

    0=(x-1)(x+1)
    0=x^2-1

  13. x=\dfrac{1}{5}, x=-\dfrac{1}{5} \\
    x-\dfrac{1}{5}=0, x+\dfrac{1}{5}=0

    0=(x-\dfrac{1}{5})(x+\dfrac{1}{5}) \\
    0=x^2-\dfrac{1}{25}

  14. x=\sqrt{7}, x=-\sqrt{7}
    x-\sqrt{7}=0, x+\sqrt{7}=0

    0=(x-\sqrt{7})(x+\sqrt{7})
    0=x^2-7

  15. x=\sqrt{11}, x=-\sqrt{11}
    x-\sqrt{11}=0, x+\sqrt{11}=0

    0=(x-\sqrt{11})(x+\sqrt{11})
    0=x^2-11

  16. x=2\sqrt{3}, x=-2\sqrt{3}
    x-2\sqrt{3}=0, x+2\sqrt{3}=0

    0=(x-2\sqrt{3})(x+2\sqrt{3})
    0=x^2-12

  17. x=3, x=5, x=8
    (x-3)=0, (x-5)=0, (x-8)=0

    \begin{array}{rrcrcrrrr} (x&-&3)(x&-&5)(x&-&8)&=&0 \\ (x^2&-&8x&+&15)(x&-&8)&=&0 \\ x^3&-&8x^2&+&15x&&&& \\ &-&8x^2&+&64x&-&120&=&0 \\ \midrule x^3&-&16x^2&+&79x&-&120&=&0 \end{array}

  18. x=-4, x=0, x=4
    x+4=0, x, x-4=0

    x(x+4)(x-4)=0
    x(x^2-16)=0
    x^3-16x=0

  19. x=-9, x+6=0, x=-2
    x+9=0, x+6=0, x+2=0

    \begin{array}{rrcrcrrrr} (x&+&9)(x&+&6)(x&+&2)&=&0 \\ (x^2&+&15x&+&54)(x&+&2)&=&0 \\ x^3&+&15x^2&+&54x&&&& \\ &+&2x^2&+&30x&+&108&=&0 \\ \midrule x^3&+&17x^2&+&84x&+&108&=&0 \end{array}

  20. x=-1, x=1, x=5
    x+1=0, x-1=0, x-5=0

    (x+1)(x-1)(x-5)=0
    (x^2-1)(x-5)=0
    x^3-5x^2-x+5=0

  21. x=-2, x=2, x=5, x=-5
    x+2=0, x-2=0, x-5=0, x+5=0

    (x+2)(x-2)(x-5)(x+5)=0
    (x^2-4)(x^2-25)=0
    x^4-29x^2+100=0

  22. x=2\sqrt{3}, x=-2\sqrt{3}, x=\sqrt{5}, x=-\sqrt{5}
    x-2\sqrt{3}=0, x+2\sqrt{3}=0, x-\sqrt{5}=0, x+\sqrt{5}=0

    (x-2\sqrt{3})(x+2\sqrt{3})(x-\sqrt{5})(x+\sqrt{5})=0
    (x^2-12)(x^2-5)=0
    x^4-17x^2+60=0

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Intermediate Algebra by Terrance Berg is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.

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