if x+1 is a factor of ax^4+bx^2+c, what is the value of a+b+c?
divide ax^4+ 0 x^3 +bx^2 + 0 x +c by (x+1)
a x^3 - a x^2 + (a+b)x - (a+b)
remainder = a + b + c which must be zero
let f(x) = ax^4 + bx^2 + c
f(-1) = 0 , since it is a factor
but f(-1)
= a+ b + c
so a+b+c = 0
LOL - do it Reiny's way !
its kind of confusing
To find the value of a+b+c, we need to use the given information that x+1 is a factor of ax^4+bx^2+c.
When a polynomial is divided by a linear factor, the remainder is zero if the factor is indeed a factor of the polynomial. So, if x+1 is a factor of ax^4+bx^2+c, we can set the polynomial equal to zero and substitute x = -1 to find the value of a+b+c.
Putting x+1 equal to zero, we have:
x + 1 = 0
x = -1
Substituting this value into the polynomial ax^4+bx^2+c, we get:
a(-1)^4+b(-1)^2+c = 0
This simplifies to:
a+b+c = 0
Therefore, the value of a+b+c is zero.