Question

Which polynomial is prime?

x3 + 3x2 – 2x – 6 x3 – 2x2 + 3x – 6 4x4 + 4x3 – 2x – 2

2x4 + x3 – x + 2

Answer 1

SOLUTION

TO DETERMINE

Which polynomial is prime

$\sf{1. \: \: {x}^{3} + 3 {x}^{2} - 2x - 6}$

$\sf{2. \: \: {x}^{3} - 2 {x}^{2} + 3x - 6}$

$\sf{3. \: \: 4{x}^{4} + 4 {x}^{3} - 2x - 2}$

$\sf{4. \: \: 2{x}^{4} + {x}^{3} - x - 2}$

CONCEPT TO BE IMPLEMENTED

Polynomial

Polynomial is a mathematical expression consisting of variables, constants that can be combined using mathematical operations addition, subtraction, multiplication and whole number exponentiation of variables

Prime Polynomial

A polynomial with integer coefficients that cannot be factored into polynomials of lower degree is called prime polynomial

EVALUATION

CHECKING FOR OPTION : 1

Here the given polynomial is

$\sf{{x}^{3} + 3 {x}^{2} - 2x - 6}$

( x + 3) is factor of this polynomial

So it is not prime polynomial

CHECKING FOR OPTION : 2

Here the polynomial is

$\sf{{x}^{3} - 2 {x}^{2} + 3x - 6}$

( x - 2 ) is a factor of the polynomial

So it is not a prime polynomial

CHECKING FOR OPTION : 3

Here the polynomial is

$\sf{4{x}^{4} + 4 {x}^{3} - 2x - 2}$

( x + 1 ) is a factor of the polynomial

So it is not a prime polynomial

CHECKING FOR OPTION : 4

Here the polynomial is

$\sf{2{x}^{4} + {x}^{3} - x - 2}$

Now the polynomial can be factorised

So this polynomial is prime polynomial

FINAL ANSWER

The correct option is

$\sf{4. \: \: 2{x}^{4} + {x}^{3} - x - 2}$

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Answer 2

$\huge \rm{ \underline{ \underline\red{ \red{A{ \orange{N{ \red{S{ \orange{W{ \red{E{ \orange{R { \red{ \:}}}}}}}}}}}}}}}}$

$\sf{ \red{Which \: polynomial \: is \: prime \: ?}}$

$\sf{ \orange{1. \: \: {x}^{3} + 3 {x}^{2} - 2x - 6} }$

$\sf{ \orange{2. \: \: {x}^{3} - 2 {x}^{2} + 3x - 6} }$

$\sf{ \orange{3. \: \: 4{x}^{4} + 4 {x}^{3} - 2x - 2}}$

$\bold{ \orange{4. \: \: 2{x}^{4} + {x}^{3} - x - 2}} \: \: \: \: \: \bold\red{\checkmark}$