Question

check whether 2x3-5x2+4x-3 is a multiple of (x-2) or not​

Answer 1

Given,

A polynomial p(x) = 2x^3-5x^2+4x-3

To find,

If p(x) is a multiple of (x-2) or not.

Solution,

We can simply solve this mathematical problem using the following process:

Mathematically,

For a certain polynomial p(x), if the value of p(x) at x = a is 0, then "a" is a root of a polynomial p(x) and (x-a) is a factor of p(x).

According to the question;

p(x) = 2x^3-5x^2+4x-3

Now,

p(2) = 2(2)^3-5(2)^2+4(2)-3

= 16 - 20 + 8 - 3

= 24-23

= 1

=> p(2) is not equal to zero

=> 2 is not a zero of the polynomial p(x)

=> (x-2) is not a factor of the polynomial p(x)

=> p(x) is not a multiple of (x-2)

Hence, p(x) is not a multiple of (x-2).

Answer 2

Answer:

Step-by-step explanation: To check whether 2x^3-5x^2+4x-3 is a multiple of (x-2) or not.

Ans:- x-2=0 [as it is a factor]

x=2

2[2]^3-5[2]^2+4[2]-3=0

16-10+8-3=0

But 1 is not equal to 0

We can conclude that (x-2) is not a factor of 2x^3-5x^2+4x-3