Question

`8x^3 +10x^2- px- 5` is divisible by `2x +1`. There is no remainder. How do you find the value of p?

Answer 1

`p = 7`

Explanation:

The remainder theorem states that if a polynomial `f(x)` is divided by `x - a`, the remainder is given by evaluating `f(a)`.

Here, `a = -1/2`, since when we solve `2x+ 1 = 0`, we get `x = -1/2`.

So,

`8(-1/2)^3 + 10(-1/2)^2 - p(-1/2) - 5 = 0`

`8(-1/8) + 10(1/4) + 1/2p - 5 = 0`

`-1 + 5/2 + 1/2p - 5 = 0`

`1/2p = 5 - 5/2 + 1`

`1/2p = 7/2`

`p = (7/2)/(1/2)`

`p = 7`

Hopefully this helps!