Question

check whether the polynomial p(x)=3x3+x2-20x+12 is a multiple of 3x-2​

Answer 1

I hope that you will get your answer. ☺☺☺

Answer 2

Given:

p(x) = 3x³+ x²-20x +12

To Find:

If the given polynomial is a multiple of 3x - 2.

Solution:

p(x) = 3x³+x²-20x+12

      = 3x - 2 = 0

    x = 2/3

p($\frac{2}{3}$) = 3 × ($\frac{2}{3}$)³+($\frac{2}{3}$)³- 20×$\frac{2}{3}$+12

      = 3 × $\frac{8}{72}$ + $\frac{4}{9}$ - $\frac{40}{3}$ + 12

      = $\frac{8}{9}$ + $\frac{4}{9} - \frac{40}{3}+\frac{12}{1}$

      = $\frac{8+4}{9}$ - 120 +108

      = 120 - 120/9

      = 0

Therefore, 3x-2 is a multiple of 3x²+3x-20x+12.