Question 15

If (x + 4) is a factor of $$x^3 + 2x^2 + bx + 68$$, what is the value of b?

Solution

Let say f(x) = $$x^3 + 2x^2 + bx + 68$$ and given (x+4) is a factor of f(x).

$$\Rightarrow f(x) = (x+4)\times k$$.................(1)

where 'k' is the quotient when f(x) is divided by (x+4).

Substituting 'x= -4' in the equation (1), we get

f(-4) = 0

$$\Rightarrow -4^3 + 2 (-4)^2 + b (-4) + 68 = 0$$

$$\Rightarrow -64 + 32 - 4b + 68 = 0$$

$$\Rightarrow 4b = 36$$

$$\Rightarrow b = 9$$.

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