Question

Show that (2x + 7) is a factor of 2x³ + 7x² – 4x – 14. Hence factorize the expression.

Answer 1

Solution :

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 ]

ii )

2x+7)2x³+7x²-4x-14(x²-2
*******2x³+7x²
____________
****************-4x-14
***************-4x -14
_______________
**********( 0 )

p(x) = (2x+7)( x²-2 )

= (2x+7)[ x² - (√2)²]

= ( 2x + 7 )( x + √2 )( x - √2 )

•••••

Answer 2

Answer:

(2x+7)(×+2)(×-2)

Step-by-step explanation:

Let f(x) = 2x^3 + 7x^2 - 4x - 14

2x + 7 = 0

2x = -7

x = -7/2

f(-7/2)=2((-7/2)^3 +7((-7/2)^2) -4(-7/2) -14

=2(-343)/8 +7(49)/4 +28/2 -14

= -343+343-56+56

_______________

4

= 0

f(-7/2)=0

2x+7 is a factor of f(x)

2x^3 + 7x^2 -4x -14 = (2x+7)(x^2 -2)

= (2x+7)(x+2)(x-2)