Q1 of 108 Page 46

Find the lowest common multiple of the following expressions:

x2 – 1; (x2 + 1) (x + 1) and x2 + x –1


Let u(x) = (x2 – 1) = (x + 1) (x – 1)

Let v(x) = (x2 + 1) (x + 1)


Let w(x) = x2 + x –1


By comparing u(x), v(x) and w(x),


The LCM is = (x + 1) (x – 1) (x2 + 1) (x2 + x –1)


= (x2 – 1) (x2 + 1) (x2 + x –1)


= (x4 – 1) (x2 + x –1)


More from this chapter

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1

Find the lowest common multiple of the following expressions:

x2 – 3x + 2 and x4 + x3 – 6x2


 1

Find the lowest common multiple of the following expressions:

(iii) 2x2 – 8 and x2 – 5x + 6


 1

Find the lowest common multiple of the following expressions:

18(6x4 + x3 – x2) and 45(2x6 + 3x5 + x4)


 2

Find the highest common factor of the following expressions:

(i) a3b4, ab5, a2b8


(ii) 16x2y2, 48x4z


(iii) x2 – 7x + 12; x2 – 10x + 21 and x2 + 2x – 15


(iv) (x + 3)2 (x – 2) and (x + 3) (x – 2)2


(v) 24(6x4 – x3 – 2x2) and 20(6x6 + 3x5 + x4)