-1
$\begingroup$

I am not sure how the following factorises to give the answer circled. How would you know that 2/21 needs to be multiplied by 3u and -7 ? Mentally I do not think I would be able to do this. Is there a trick to use ?

enter image description here

  • 1
    Well,$$\frac{6u^7-14u^6}{21}=\frac{1}{21}\cdot(6u^7-14u^6)=\frac{1}{21}\cdot 2 u^6(3u-7)$$ – 2017-02-02

1 Answers 1

1

We can factor the numerator as: $$6u^7-14u^6 = (2u^6)(3u)-(2u^6)(7) =(2)(3u^7-7u^6)= (2)(u^6)(3u-7) $$ Now dividing by $21$ and rearranging gives us $$\boxed {\frac {6u^7-14u^6}{21} = \frac {2}{21} u^6 (3u-7)}$$ Hope it helps .