Algebra Demystified 2nd Ed

166 algebra De mystif ieD

14. 15x1/2 − 8x1/4 + 1 =


15. 14 xx –  = 3  – 


16. 25x^6 + 20x^3 + 4 =


17. xx +  69 +  =

✔SOLUTIONS

1. x^4 − 3x^2 + 2 = (x^2 − 2)(x^2 − 1)


2. x^10 − 3x^5 + 2 = (x^5 − 2)(x^5 − 1)


3. x2/5 − 3x1/5 + 2 = (x1/5 − 2)(x1/5 − 1)


4. x−6 − 3x−3 + 2 = (x−3 − 2)(x−3 − 1)


5. x1/2 − 3x1/4 + 2 = (x1/4 − 2)(x1/4 − 1)


6. x^4 + 10x^2 + 9 = (x^2 + 9)(x^2 + 1)


7. x^6 − 4x^3 − 21 = (x^3 − 7)(x^3 + 3)


8. 4x^6 + 4x^3 − 35 = (2x^3 + 7)(2x^3 − 5)


9. 10x^10 + 23x^5 + 6 = (10x^5 + 3)(x^5 + 2)


10. 9x^4 − 6x^2 + 1 = (3x^2 − 1)(3x^2 − 1) = (3x^2 − 1)^2


11. x2/7 − 3x1/7− 18 = (x1/7 − 6)(x1/7 + 3)


12. 6x2/3 − 7x1/3 − 3 =(2x1/3 − 3)(3x1/3 + 1)


13. x1/3 + 11x1/6 + 10 = (x1/6 + 10)(x1/6 + 1)


14. 15x1/2 − 8x1/4 + 1 = (3x1/4 − 1)(5x1/4 − 1)
    15.^14 xx^ –  – ^31 =^43 xx^11 –  //^21 –   (= ^21 xx^21 – )(^73 /^2 +  ))
    =2()xx–  13 ()7+


15. 25x^6 + 20x^3 + 4 = (5x^3 + 2)(5x^3 + 2) = (5x^3 + 2)^2


16. xx^ +  + ^ = xx^11 + ^69 //^21 +   (= xx^21 + ^33 )( /^2 + 69)
    =()xx^12 /+ ^2 = ()+ 

2

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Factoring to Simplify a Larger Family of Fractions

Now that we have more factoring skills, we can use them to simplify a larger

family of fractions. To write a fraction in its lowest terms, we factor the numer-

ator and denominator and divide out any like factors.