the area of a rectangle is given by 6x²+19x+15. factor to find binomial that represent the length and width of the rectangle.​

Explanation:

Step-by-step explanation:Explanation:

We have that

6

x

2

+

19

x

+

15

=

6

x

2

+

10

x

+

9

x

+

15

=

2

x

⋅

(

3

x

+

5

)

+

3

⋅

(

3

x

+

5

)

=

(

2

x

+

3

)

⋅

(

3

x

+

5

)

Step-by-step explanation:

6x² + 19 x +15 can be factor as (x-root1 )( x-root2)* coefficient of x²

use quadratic equation to fid the roots, x = (-b±√b²-4ac)/2a

6x² + 19 x +15 =0

x= (-19 ±√19²-4*6*15) / 2*6

x= (-19 ± √1)/ 12

x= (-19+ 1)/12 = -18/12 = -3/2

and

x= (-19-1)/12 = -20/12 = -5/3

6x² + 19 x +15 = 6*(x+(3/2)) (x+(5/3))

the length and with of the rectangle could be any combination of the factors of 6 and the (x+(3/2)) (x+(5/3))

if we consider 6 =2*3 we have length and width 2x+3 and 3x+5

because 2*[x+(3/2)]*3[ x+(5/3)]

if we consider 6 = 3*2 we have length and width 3x+(9/2) and 2x+(10/3)

because 3*[x+(3/2)]*2[ x+(5/3)]

if we consider 6= 6*1 we have length and width 6x+9 and x+(5/3)

because 6*[x+(3/2)]*1[ x+(5/3)]

if we consider 6= 1*6 we have length and width x+(3/2) and 6x+10

because 1*[x+(3/2)]*6[ x+(5/3)]