if cx³+dx²-5c-6 is divisible by x+1 & 2x-3,find the value of c and d

Question

if cx³+dx²-5c-6 is divisible by x+1 & 2x-3,find the value of c and d

Answer 1

Hi Liam,

If we know two binomial factors of the cubic, there can be at most one more factor of cx³ + dx² - 5c - 6. That factor looks like (ax+b) and if I knew what a and b were, I'd know what c and d are.

So let's expand. (x+1)(2x-3)(ax+b) is 2ax^3 + (2b-a)x^2 + (-3a-b)x - 3b.

Now we can compare that to the other cubic by matching up each of the four coefficients and work with four much easier equations:

2a = c

d = 2b-a

0 = -3a - b

-5c - 6 = -3b