Question

Find the remainder when 2x2-3x+5 is divided by 2x-3.does it exactly divide the polynomial? state reason​

Answer 1

Answ

Step-by-step explanation:

Let p(x) = 2x2 – 3x + 5

As we know by Remainder Theorem,

If a polynomial p(x) is divided by a linear polynomial (x – a) then, the remainder is p(a)

⇒ Remainder of p(x) when divided by 2x – 3 is  

= 5

⇒ Remainder of 2x2 – 3x + 5 when divided by 2x – 3 is 5.

As on dividing the given polynomial by 2x – 3, we get a non–zero remainder, therefore, 2x – 3 does not completely divide the polynomial.

∴ It is not a factor.

Answer 2

Step-by-step explanation:

Given :-

2x²-3x+5 is divided by 2x-3

To find :-

Find the remainder when 2x²-3x+5 is divided by 2x-3.Does it exactly divide the polynomial?

Solution :-

Given polynomial = 2x²-3x+5

Let P(x) = 2x²-3x+5

Given divisor = 2x-3

We know that

By Remainder Theorem,

If P(x) is divided by 2x-3 then the remainder = P(3/2)

Since 2x-3 = 0

=> 2x = 3

=> x = 3/2

Now,

The remainder = P(3/2)

=> 2(3/2)²-3(3/2)+5

=> 2(9/4)-(9/2)+5

=> (9/2)-(9/2)+5

=> [(9-9)/2] +5

=> (0/2)+5

=> 0+5

=> 5

The remainder = 5

So The given polynomial is not exactly divisible by 2x-3.

Reason :-

If a polynomial P(x) is divided by g(x) exactly then the remainder is 0.

Answer :-

1) The remainder is 5

2) It is not exactly divisible by the polynomial.

Check :-

On Dividing P(x) by 2x-3 then

2x-3 ) 2x²-3x+5 ( x

2x²-3x

(-) (+)

_________

5

__________

The remainder = 5

Used formulae:-

Remainder Theorem:-

Let P(x) be a polynomial of the degree greater than or equal to 1 and x-a is another linear polynomial if P(x) is divided by x-a then the remainder is P(a).

→If a polynomial P(x) is divided by g(x) exactly then the remainder is 0.Then g(x) is a factor of P(x).