Question

If (x + a) is a factor of x3+ ax2 – 2x + a + 4. Find the value of a.
3
4
1)
4.
3
3
2) -
3)
1
4
3

Answer 1

Answer:

x^3+ax^2-2x+a+4 Must be divisible by x+a

so,(

=x^2–2 is quotient and (a+4)-(-2a) is remainder

But the polynomial is divisible so the remainder should be 0

Thus , (a+4)-(-2a)=0

=>(a+4+2a)=0

=>3a+4=0

=>a=-4/3

Answer 2

If (x + a) is a factor of x3+ ax2 – 2x + a + 4. Find the value of a.

Solution:-

x^3+ ax^2 – 2x + a + 4 Must be divisible by x + a

So, $\frac{(x^3 + ax^2 - 2x + a + 4)}{x + a}$

= x^2 - 2 is quotient and (a + 4) - (- 2a) is reminder

But the polynomial is divisible so the reminder should be 0.

Thus,

(a + 4) - (-2a) = 0

=> (a + 4 + 2a) = 0

=> 3a + 4 = 0

=> a = $\frac{-4}{3}$