can any one factories each of them question 21 and 23
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21)
Given quadratic polynomial is 2x2 + (5/6)x + (1/12)
Let's take LCM and simplify the above polynomial
2x2 + (5/6)x + (1/12) = (1/12)[24x2 + 10x + 1]
Now we will factorise the quadratic polynomial by splitting the middle term
(1/12)[24x2 + 10x + 1] = (1/12)[24x2 + 6x + 4x + 1]
= (1/12)[6x(4x+1) + 1( 4x + 1)]
= (1/12)[(4x+1) (6x + 1)]
23)
We have : x 3 - x 2 + a x + x - a - 1 , So
⇒ x 3 + a x + x - x 2 - a - 1
⇒ ( x 3 + a x + x ) + ( - x 2 - a - 1 )
⇒ x ( x 2 + a + 1 ) - 1 ( x 2 + a + 1 )
⇒ ( x - 1 ) ( x 2 + a + 1 )
Given quadratic polynomial is 2x2 + (5/6)x + (1/12)
Let's take LCM and simplify the above polynomial
2x2 + (5/6)x + (1/12) = (1/12)[24x2 + 10x + 1]
Now we will factorise the quadratic polynomial by splitting the middle term
(1/12)[24x2 + 10x + 1] = (1/12)[24x2 + 6x + 4x + 1]
= (1/12)[6x(4x+1) + 1( 4x + 1)]
= (1/12)[(4x+1) (6x + 1)]
23)
We have : x 3 - x 2 + a x + x - a - 1 , So
⇒ x 3 + a x + x - x 2 - a - 1
⇒ ( x 3 + a x + x ) + ( - x 2 - a - 1 )
⇒ x ( x 2 + a + 1 ) - 1 ( x 2 + a + 1 )
⇒ ( x - 1 ) ( x 2 + a + 1 )
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