Question

When $$2x^3 - 9x^2 + 10x - p$$ is divided by $$(x + 1)$$, the remainder is $$- 24.$$ Find the value of $$p.$$

Answer 1

Given

$$f(x) = 2x^3 - 9x^2 + 10x - p$$

And remainder $$r=-24$$, when $$f(x)$$ is divided by $$(x+1)$$

Let us assume $$x + 1 = 0\Rightarrow x = -1$$

$$\therefore$$ By remainder theorem,

$$f(-1) =-24\\\Rightarrow 2(-1)^3 - 9(-1)^2 + 10(-1) -p=-21\\\Rightarrow -2 - 9 - 10 -p+24=0\\\Rightarrow -21+24-p=0\\\Rightarrow 3-p=0\\\Rightarrow p=3$$

Therefore, the value of $$p$$ is $$3$$.