Question

The function f(x)=ax³ +4x²+bx-2,where a and b are constants, is such that 2x-1 is a factor. Given that the remainder when f(x) is divided by x-2 is twice the remainder when f(x) is divided by x+1,find the value of a and b.
PLS EXPLAIN IN DETAIL
I NEED YOUR HELP PLSSSSS

Answer 1

Answer:

Well the aswer would be too long

but i will try to help

Divide the function by 2x-1,you will find that the remainder is some mixture of the constants a and b.

Since we know that 2x-1 is a factor of the function,which means that it leaves no remainder which means that the mixture of the constants you found will be an equation that looks something like something into a and something into b is equal to 0 cuz remainder is zero.

then find the remainders of the other two factors.

Remainders of x-2 and x+1.

This too will be a mix of constants a and b.

Now using the relation (Remainder of x-2 is twice remainder of x+1)

equate,remainder of x+1=2×remainder of x-2.

With this you will find and equation of constants a and b.

Now subtitute values of a or b in the first equation.