Question

if(x) =2x^3+5x^2-3x+2 is divided by 2x-1 find its reminder​

Answer 1

Step-by-step explanation:

For this put x=1 in polynomial,

P(1)=2(1) ^3+5(1) ^2 −3(1)−2

⇒P(1)=2

So, remainder is 2.

Answer 2

$\huge\color{red}{\mathfrak{Question}}$

If(x) = 2x³ + 5x² - 3x + 2 is divided by 2x-1 find its reminder

$\color{blue}\large\underline{\underline{answer}}$

By using reminder theorem

Where, 2x - 1 = 0

=> 2x = 1

$= > x = \frac{1}{2}$

$p(x) = 2 {x}^{3} + 5 {x}^{2} - 3x + 2$

$p( \frac{1}{2} ) = 2( \frac{1}{2} )^{3} + 5( \frac{1}{2} )^{2} + 3( \frac{1}{2} ) + 2$

$p( \frac{1}{2} ) = 2( \frac{1}{8} ) + 5( \frac{1}{4} ) + \frac{3}{2} + 2$

$p( \frac{1}{2} ) = \frac{2}{8} + \frac{5}{4} + \frac{3}{2} + 2$

$p( \frac{1}{2} ) = \frac{1 + 5 + 6 + 8}{4}$

$p( \frac{1}{2} ) = \frac{20}{4} = 5$

Hence, the reminder is 5