Question

Show that 2x + 7 is a factor of 2x3 + 7x2 – 14x – 14. Hence, factorise 2x2 + 7x2 – 4x – 14.​

Answer 1

Let p(x) = 2x³+7x²-4x-14

To show 2x+7 is a factor ,

Take , 2x + 7 = 0

2x = -7

=> x = -7/2

put x = -7/2 in p(x )

i ) p(-7/2 ) = 2(-7/2)³+7(-7/2)²-4(-7/2)-14

= -343/4 + 343/4 + 14 - 14

= 0

Therefore ,

2x + 7 is a factor of p(x).

[ By factor theorem ]

Now,

2x+7)2x³+7x²-4x-14(x²-2

2x³+7x²

p(x) = (2x+7)( x²-2 )

= (2x+7)[ x² - (√2)²]

= ( 2x + 7 )( x + √2 )( x - √2 )

Answer 2

Answer:

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