Question

find the value of b for which (2x+3) is a factor of

Answer 1

Given polynomial,

2x³+9x²-x-b

Let f(x)=2x³+9x²-x-b

2x+3 is a factor of f(x)

Let g(x)=2x+3

2x+3=0

x=-3/2

Put x=-3/2 in f(x)

2(-3/2)³+9(-3/2)²-(-3/2)-b=0

2(-27/8)+9(9/4)+3/2-b=0

-27/4+81/4+3/2-b=0

(-27+81)/4+3/2-b=0

54/4+3/2-b=0

(54+6)/4-b=0

60/4-b=0

→b=60/4

Hope it helps.. ….

Answer 2

Hey there !!

2x³+9x²-x-b

p(x)=2x³+9x²-x-b

2x+3 is a factor of p(x)


g(x) = 2x+3

x = -3/2

Lets put the value of x in p(x) :-


2 × -3/2³+9 ×-3/2 ² - (-3/2) -b = 0

2 × -27/8 +9 × 9/4 +3/2 - b=0

-27/4 + 81/4 + 3/2 - b = 0

54/4+3/2-b=0

LCM of 2 and 4 is 4.

54/4 +6/4 -b = 0

60/4 - b=0

Hence ,

b = 60/4