Question

im confused of this Use the remainder theorem and synthetic division to find f(k) for the given value of k. f(x) = -2x3 - 12x2 - 10x – 8; k= -5 f(-5) =D

Answer 1

Solution-

According to remainder theoram, if a polynomial f(x) is divided by linear polynomial (x- a) , the remainder will be equivalent to f(a)

Consider the function -

f(x) =-2x³ -12x² -10x -8

Let perform synthetic division by k = - 5 to find f(k) .

Steps of synthetic division-

1) Bring the digit -2 down.

2) Multiply -2 with -5 to get 10 and then adding 10 with -12 to get -2.

3) Multiply -2 with -5 to get -10 and then adding -10 with 10 to get 0.

4) Multiply 0 with -5 to get 0 and then adding 0 with -8 to get -8 as remainder.

So, reaminderr= -8

And by reminder theoram , remainder =f(-5) = -8

Hence, f(-5) = -8