If (ax+2)(bx+7) = 15xsquared + cx +14 for all values of x, and a+b =8, what are the two possible values for c?

The two possible values for c are 31 and 41

Step-by-step explanation:

Given Expression:

a + b = 8

To expand,

Multiply a x with (b x + 7) =  

Multiply 2 with (b x + 7) = 2 b x +14

Now, combining the above, we get

When comparing both sides, we get

a b = 15, 7 a + 2 b = c

Now, substitute above value in a + b = 8. So,

Factorising above, we get the equation as

       (b - 3) (b - 5) = 0

b = 3 and 5

If b = 3, then

If b = 5, then

If a = 3, b = 5

c =7 a + 2 b = 7 (3) + 2 (5) = 21 + 10 = 31

If a = 5, b = 3

c =7 (5) +2 (3) = 35 + 6 = 41

Therefore, the values of ‘c’ are 31 and 41 .