Question

find the remainder when 9x³-3x²+x-5 is divided by x-⅔​

Answer 1

x-2/3=0

x=2/3

f(x)=9x3-3x2+x-5

f(2/3)=9(2/3)(2/3)(2/3)-3(2/3) (2/3)+(2/3)-5

=8/3-4/3+2/3-5

=(8-4+2-15)/3

=-9/3

=-3

The remainder is -3

Answer 2

Answer:

- 3

Step-by-step explanation:

Let p(x) be 9x³ - 3x² + x - 5

g(x) = x - 2/3

Here we can use the Remainder Theorem, which states:

When the polynomial p(x) is divided by the linear polynomial x - a the the remainder obtained is p(a).

Let us find the zero of g(x)

x - 2/3 = 0

x = 2/3

Hence we substitute x = 2/3 to find the remainder:

$p(\frac{2}{3} ) = 9(\frac{2}{3})^3 - 3(\frac{2}{3})^2 + \frac{2}{3} - 5\\\\= 9(\frac{8}{27}) - 3(\frac{4}{9}) + \frac{2}{3} - 5\\\\=\frac{8}{3} - \frac{4}{3} + \frac{2}{3} - 5\\\\=\frac{6}{3} -5\\\\= 2 - 5\\\\= -3$

Hence, the remainder obtained when 9x³ - 3x² + x - 5 is divided by x - 2/3 is - 3