If 2x+5 is a factor of 6x2+19x+c what is the value of c?

1 Answer
Nov 29, 2016

c=10

Explanation:

With the information provided we can write:

6x2+19x+c=(2x+5)(ax+b)

Cross multiplying the terms on the right of the equation gives:

6x2+19x+c=2ax2+5ax+2bx+5b

6x2+19x+c=2ax2+(5a+2b)x+5b

Therefore we know:

6x2=2ax2 Solving for a gives.

6x2x2=2ax2x2

6=2a

2a2=62

a=3

Substituting this back into the equation gives:

6x2+19x+c=23x2+(53+2b)x+5b

6x2+19x+c=6x2+(15+2b)x+5b

Therefore we know:

19x=(15+2b)x Solving for b gives:

19xx=(15+2b)xx

19=15+2b

1915=1515+2b

4=2b

2b2=42

b=2

Substituting this back into the equation gives:

6x2+19x+c=6x2+(15+22)x+52

6x2+19x+c=6x2+(15+4)x+10

6x2+19x+c=6x2+19x+10

Therefore c=10