Q1 of 108 Page 46

Find the lowest common multiple of the following expressions:

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


Let u(x) = 18(6x4 + x3 – x2)

= 18 x2(6x2 + x –1)


Let us solve the inner quadratic equation,


6x2 + x –1 = 0


6x2 + x - 1 = 0


6x2 + 3x - 2x - 1 = 0


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


(3x – 1) (2x + 1) = 0


So u(x) = 18 x2(3x – 1) (2x + 1)


Let v(x) = 45(2x6 + 3x5 + x4)


= 45 x4(2x2 + 3x + 1)


Let us solve the inner quadratic equation,


2x2 + 3x + 1 = 0


2x2 + 2x + x + 1 = 0


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


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


So v(x) = 45 x4(2x + 1) (x + 1)


By comparing the above equation, we get


LCM = 90 x4(2x + 1) (x + 1) (3x – 1)


More from this chapter

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1

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 1

Find the lowest common multiple of the following expressions:

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 2

Find the highest common factor of the following expressions:

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


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 3

If u(x) = (x – 1)2 and v(x) = (x2 – 1) the check the true of the relation LCM × HCF = u(x) × v(x).