Which polynomial has (3x + 2) as a binomial factor?
6x³+ 3x² + 4x + 2
12x²+ 15x + 8x + 10
18x³- 12x² + 9x - 6
21x⁴+ 7x³ + 6x + 2

Solution:

Given 3x + 2 is a factor

So, the required polynomial must satisfy the equation x = -2/3

1. For the polynomial 6x³+ 3x²+ 4x + 2

= 6(-2/3)(-2/3)(-2/3) +3(-2/3)(-2/3) + 4(-2/3) +2

= -16/9 + 4/3 - 8/3 + 2

= {-16 + 12 - 24 + 18 }/9

= -10/9

2. 12x² + 15x + 8x + 10

= 12(-2/3)(-2/3) + 15(-2/3) + 8(-2/3) + 10

= 16/3 - 30/3 - 16/3 + 30/3

= 0

Hence, this is the polynomial whose binomial factor is 3x + 2

Which polynomial has (3x + 2) as a binomial factor?

Summary:

12x² + 15x + 8x + 10 is the polynomial whose binomial factor is 3x + 2.