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

1 Answer
Nov 29, 2016

c = 10

Explanation:

With the information provided we can write:

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

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

6x^2 + 19x + c = 2ax^2 + 5ax + 2bx + 5b

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

Therefore we know:

6x^2 = 2ax^2 Solving for a gives.

(6x^2)/x^2 = (2ax^2)/x^2

6 = 2a

(2a)/2 = 6/2

a = 3

Substituting this back into the equation gives:

6x^2 + 19x + c = 2*3x^2 + (5*3 + 2b)x + 5b

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

Therefore we know:

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

(19x)/x = ((15 + 2b)x)/x

19 = 15 + 2b

19 - 15 = 15 - 15 + 2b

4 = 2b

(2b)/2 = 4/2

b = 2

Substituting this back into the equation gives:

6x^2 + 19x + c = 6x^2 + (15 + 2*2)x + 5*2

6x^2 + 19x + c = 6x^2 + (15 + 4)x + 10

6x^2 + 19x + c = 6x^2 + 19x + 10

Therefore c = 10