Question

find the value of a, if X + a is a factor.
x³ + ax² - 2x + a + 4​

Answer 1

SOLUTION

The given polynomial

=)p(x)= x^3+ax^2-2x+a+4

since (x+a) is a factor of this polynomial, then

=) x+a= 0

=) x= -a

p(-a)=0

$= > {a}^{3} + a( - a) {}^{2} - 2( - a) + a + 4 = 0 \\ = > - a {}^{3} + a {}^{3} + 2a + a + 4 = 0 \\ = > 3a + 4 = 0 \\ = > 3a = - 4 \\ = > a = - \frac{4}{3}$

HOPE it helps ✔️

Answer 2

Answer:

a = -(4/3)

Step-by-step explanation:

Here, x - a = 0

x=-a

p(a)= (-a)^3 + a.(-a)^2 - 2.(-a)+ a + 4

=-a^3 +a^3 +2a + a + 4

=3a + 4

Therefore, a= -(4/3)