Question

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

Answer 1

Answer:

Hello !,

p(x)=  $2x^{3} -5x^{2} +4x-3$

(x-2) => factor.

x= 2 =>zero of p(x).

hence, p(2)=  $2(2)^{3} -5(2)^{2} +4(2)-3$

                  = 2(8) -5(4)+ 8 -3

                  = 16 -20 +8 -3

                  =  -4 +8 -3    =  4 -3

                  = 1.

Therefore (x-2) isn't a factor of p(x) ,

and so p(x)  isn't a multiple of (x-2).

Answer 2

2x³ - 5x² + 4x - 3 is not a multiple of x - 2

Given :

The polynomial 2x³ - 5x² + 4x - 3

To find :

Check whether 2x³ - 5x² + 4x - 3 is a multiple of x - 2 or not

Solution :

Step 1 of 3 :

Write down the given polynomial

Let the given polynomial = p(x)

Then p(x) = 2x³ - 5x² + 4x - 3

Step 2 of 3 :

Find the remainder when 2x³ - 5x² + 4x - 3 is divided by x - 2

Let g(x) = x - 2

For Zero of the polynomial g(x) we have

g(x) = 0

⇒ x - 2 = 0

⇒ x = 2

So the remainder when 2x³ - 5x² + 4x - 3 is divided by x - 2

= p(2)

= 2 × 2³ - 5 × 2² + 4 × 2 - 3

= 16 - 20 + 8 - 3

= - 4 + 5

= 1

Step 3 of 3 :

Check whether 2x³ - 5x² + 4x - 3 is a multiple of x - 2 or not

Since the remainder = 1 ≠ 0

Hence 2x³ - 5x² + 4x - 3 is not a multiple of x - 2

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