Question

If polynomial 3x^3 – 2x^2 + 4x + 1 is divided by x - 2, then remainder is​

Answer 1

Answer:

25 is the remainder..........

Answer 2

SOLUTION

TO DETERMINE

The remainder when

$\sf{3 {x}^{3} - 2 {x}^{2} + 4x + 1 \: \: is \: divided \: by \: \:( x - 2)}$

EVALUATION

Let

$\sf{f(x) = 3 {x}^{3} - 2 {x}^{2} + 4x + 1 }$

$\sf{g(x) = x - 2}$

For Zero of the polynomial g(x) we have

$\sf{g(x) = 0}$

$\sf{ \implies \: x - 2 = 0}$

$\sf{ \implies \: x = 2}$

So by the Remainder Theorem the required Remainder when f(x) is divided by g(x) is

$\sf{ = f(2) }$

$\sf{ = 3 \times {(2)}^{3} - 2 \times {(2)}^{2} + 4 \times 2 + 1 }$

$\sf{ = (3 \times 8) - (2 \times 4)+ (4 \times 2 \: )+ 1 }$

$\sf{ =24 - 8+ 8+ 1 }$

$= 25$

FINAL ANSWER

Hence the required Remainder = 25

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

1. If x+1/x=3 then, x^7+1/x^7=

https://brainly.in/question/23295932 

2. A polynomial is an expression, the sum of a finite number of terms, form axN, Exponent n is always =---- 

https://brainly.in/question/29065169