Answer Key 10.8
- [latex]x=5, x=2[/latex]
[latex]x-5=0, x-2=0[/latex][latex]0=(x-5)(x-2)[/latex]
[latex]0=x^2-7x+10[/latex] - [latex]x=3, x=6[/latex]
[latex]x-3=0, x-6=0[/latex][latex](x-3)(x-6)=0[/latex]
[latex]0=x^2-9x+18[/latex] - [latex]x=20, x=2[/latex]
[latex]x-20=0, x-2=0[/latex][latex]0=(x-20)(x-2)[/latex]
[latex]0=x^2-22x+40[/latex] - [latex]x=13, x=1[/latex]
[latex]x-13=0, x-1=0[/latex][latex]0=(x-13)(x-1)[/latex]
[latex]0=x^2-14x+13[/latex] - [latex]x=4, x=4[/latex]
[latex]x-4=0, x-4=0[/latex][latex]0=(x-4)(x-4)[/latex]
[latex]0=x^2-8x+16[/latex] - [latex]x=0, x=9[/latex]
[latex]x-9=0, x[/latex][latex]x(x-9)=0[/latex]
[latex]0=x^2-9x[/latex] - [latex]x=\dfrac{3}{4}, x=\dfrac{1}{4} \\[/latex]
[latex]x-\dfrac{3}{4}=0, x-\dfrac{1}{4}=0[/latex][latex]0=\left(x-\dfrac{3}{4}\right)\left(x-\dfrac{1}{4}\right) \\[/latex]
[latex]0=x^2-x+\dfrac{3}{16}[/latex] - [latex]x=\dfrac{5}{8}, x=\dfrac{5}{7} \\[/latex]
[latex]x-\dfrac{5}{8}=0, x-\dfrac{5}{7}=0[/latex][latex]0=\left(x-\dfrac{5}{8}\right)\left(x-\dfrac{5}{7}\right) \\[/latex]
[latex]0=x^2-\dfrac{75}{56}x+\dfrac{25}{56}[/latex] - [latex]x=\dfrac{1}{2}, x=\dfrac{1}{3} \\[/latex]
[latex]x-\dfrac{1}{2}=0, x-\dfrac{1}{3}=0[/latex][latex]0=\left(x-\dfrac{1}{2}\right)\left(x-\dfrac{1}{3}\right) \\[/latex]
[latex]0=x^2-\dfrac{5}{6}x+\dfrac{1}{6}[/latex] - [latex]x=\dfrac{1}{2}, x=\dfrac{2}{3} \\[/latex]
[latex]x-\dfrac{1}{2}=0, x-\dfrac{2}{3}=0[/latex][latex]0=\left(x-\dfrac{1}{2}\right)\left(x-\dfrac{2}{3}\right) \\[/latex]
[latex]0=x^2-\dfrac{7}{6}x+\dfrac{1}{3}[/latex] - [latex]x=5, x=-5[/latex]
[latex]x-5=0, x+5=0[/latex][latex]0=(x-5)(x+5)[/latex]
[latex]0=x^2-25[/latex] - [latex]x=1, x=-1[/latex]
[latex]x-1=0, x+1=0[/latex][latex]0=(x-1)(x+1)[/latex]
[latex]0=x^2-1[/latex] - [latex]x=\dfrac{1}{5}, x=-\dfrac{1}{5} \\[/latex]
[latex]x-\dfrac{1}{5}=0, x+\dfrac{1}{5}=0[/latex][latex]0=(x-\dfrac{1}{5})(x+\dfrac{1}{5}) \\[/latex]
[latex]0=x^2-\dfrac{1}{25}[/latex] - [latex]x=\sqrt{7}, x=-\sqrt{7}[/latex]
[latex]x-\sqrt{7}=0, x+\sqrt{7}=0[/latex][latex]0=(x-\sqrt{7})(x+\sqrt{7})[/latex]
[latex]0=x^2-7[/latex] - [latex]x=\sqrt{11}, x=-\sqrt{11}[/latex]
[latex]x-\sqrt{11}=0, x+\sqrt{11}=0[/latex][latex]0=(x-\sqrt{11})(x+\sqrt{11})[/latex]
[latex]0=x^2-11[/latex] - [latex]x=2\sqrt{3}, x=-2\sqrt{3}[/latex]
[latex]x-2\sqrt{3}=0, x+2\sqrt{3}=0[/latex][latex]0=(x-2\sqrt{3})(x+2\sqrt{3})[/latex]
[latex]0=x^2-12[/latex] - [latex]x=3, x=5, x=8[/latex]
[latex](x-3)=0, (x-5)=0, (x-8)=0[/latex][latex]\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 \\ \hline x^3&-&16x^2&+&79x&-&120&=&0 \end{array}[/latex]
- [latex]x=-4, x=0, x=4[/latex]
[latex]x+4=0, x, x-4=0[/latex][latex]x(x+4)(x-4)=0[/latex]
[latex]x(x^2-16)=0[/latex]
[latex]x^3-16x=0[/latex] - [latex]x=-9, x+6=0, x=-2[/latex]
[latex]x+9=0, x+6=0, x+2=0[/latex][latex]\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 \\ \hline x^3&+&17x^2&+&84x&+&108&=&0 \end{array}[/latex]
- [latex]x=-1, x=1, x=5[/latex]
[latex]x+1=0, x-1=0, x-5=0[/latex][latex](x+1)(x-1)(x-5)=0[/latex]
[latex](x^2-1)(x-5)=0[/latex]
[latex]x^3-5x^2-x+5=0[/latex] - [latex]x=-2, x=2, x=5, x=-5[/latex]
[latex]x+2=0, x-2=0, x-5=0, x+5=0[/latex][latex](x+2)(x-2)(x-5)(x+5)=0[/latex]
[latex](x^2-4)(x^2-25)=0[/latex]
[latex]x^4-29x^2+100=0[/latex] - [latex]x=2\sqrt{3}, x=-2\sqrt{3}, x=\sqrt{5}, x=-\sqrt{5}[/latex]
[latex]x-2\sqrt{3}=0, x+2\sqrt{3}=0, x-\sqrt{5}=0, x+\sqrt{5}=0[/latex][latex](x-2\sqrt{3})(x+2\sqrt{3})(x-\sqrt{5})(x+\sqrt{5})=0[/latex]
[latex](x^2-12)(x^2-5)=0[/latex]
[latex]x^4-17x^2+60=0[/latex]
