Question

check whether the polynomial q(x) =4x^3+4x^2-x-1 is a multiple of2x+1​

Answer 1

Answer:

Step-by-step explanation:

LET q ( x ) = 4x³ + 4x² - x - 1

If ( 2x - 1 ) is a factor of q ( x ) , then 2x - 1 = 0 ⇒ x = 1/2.

On substituting,

q ( 1/2 ) = 4 ( 1/2 )³ + 4 ( 1/2 )² - ( 1/2 ) - 1

⇒ 4 ( 1/8 ) + 4 ( 1/4 ) - 1/2 - 1

⇒ 1/2 + 1 - 1/2 - 1

⇒ 0

∴ ( 2x - 1 ) is a multiple ( factor ) of q ( x ) .