Question

15x³ +7x -2x² ÷ -2 +3x devide it and give correct remainder​

Answer 1

Answer:

$7\frac{1}{9}$

Step-by-step explanation:

We will use remainder theorem:

When a polynomial a(x) is divided by a linear polynomial b(x) whose zero is x = k, the remainder is given by r = a (k)

The remainder theorem formula is: p (x) = (x-c)·q (x) + r (x).

The basic formula to check the division is: Dividend = (Divisor × Quotient) + Remainder,

Basically we take the 0 of a polynomial and put it into the value of the variable in the other polynomial to get the remainder

p(x) =15x³ -2x²+7x

g(x)= -2 +3x

By trial and error we find zero of g(x) as 2/3.

Now we put 2/3 as value of x in p(x)

p(2/3) = 15 (2/3)³ - 2(2/3)²+7(2/3)

=15*8/27 - 2*4/9 + 14/3

=120/27 - 8/9 +14/3

=2*2*2*3*5/3*3*3 - 8/9 +14/3

=40/9-8/9+14/3

=$\frac{40}{9}-\frac{8}{9} +\frac{32}{9} = \frac{40- 8 +32}{9} = \frac{64}{9}$

$7\frac{1}{9}$