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Question
Factorise : (a2 - 3a) (a2 - 3a + 7) + 10
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Solution
(a2 - 3a) (a2 - 3a + 7) + 10
Let us assume , a2 - 3a = x
Then, our polynomial becomes,
( a2 - 3a )( a2 - 3a + 7 ) + 10
= x( x + 7 ) + 10
= x2 + 7x + 10
= x2 + 5x + 2x + 10
= x( x + 5 ) + 2 ( x + 5 )
= ( x + 5 )( x + 2 )
By resubstituting the value of x,
= (a2 - 3a + 5)( a2 - 3a + 2 )
Now, a2 - 3a + 5 will have no factor as discriminant is -11 that is less than 0.
And,
∴ a2 - 3a + 2 = a2 - 2a - a + 2 = a( a - 2) - 1(a - 2) = (a - 1)(a - 2)
So, factor of given polynomial are,
a2 - 3a + 2 = a2 - 2a - a + 2
= (a2 - 3a + 5)(a - 1)(a - 2)
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