when f(x)=2x^3−11x^3−4x+a is divided by x+2, the remainder is −4. What is the value of a
By the Remainder Theorem, f(-2) = -4. So, evaluate f(x) at x = -2 and solve for a.
Or, do a synthetic division and see what the remainder is. Set that equal to -4 and solve for a.
i get -56 but how do i know this is right, when i plug -2 into equation i get 24
As it is written,
f(-2) = 80+a
So, 80+a = -4
means a = -84
But, there is apparently a typo in f(x). If we set
f(x) = 2x^3−11x^2−4x+a
f(-2) = -52+a = -4
so, a = 48
So, how did you come by your results? I showed you mine. Show me yours.
i did synthetic division and got to 52 and since the remainder is -4 i made a= -56
the multiple choice answers are
a)48
b)56
c)48
d)-56
When you do the synthetic division, there will be an "a" in the remainder. The remainder is -52+a
So, you set -52+a = -4 and get a=48
The bottom row of the division is
2 -15 26 -52+a
To find the value of "a" in the given equation, we need to use the remainder theorem. According to the remainder theorem, if a polynomial f(x) is divided by a divisor (x - c), the remainder is equal to f(c).
In this case, the divisor is (x + 2), which means that c = -2. The remainder is given as -4. So, we can set up the equation as follows:
f(-2) = -4
Now, plug in -2 for x in the equation f(x) = 2x^3 - 11x^2 - 4x + a:
f(-2) = 2(-2)^3 - 11(-2)^2 - 4(-2) + a
Simplify the equation:
f(-2) = 2(-8) - 11(4) + 8 + a
f(-2) = -16 - 44 + 8 + a
f(-2) = -52 + 8 + a
Now, substitute the given remainder -4 for f(-2):
-4 = -52 + 8 + a
Solve for 'a' by rearranging the equation:
-4 + 52 - 8 = a
40 = a
Therefore, the value of 'a' is 40.