Question

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

Answer 1

Answer:

Friends here is your answer.

Step-by-step explanation:

Given, p(x)=x

3

−5x

2

+4x−3,

g(x)=x−2

=>x−2=0

=>x=2

Now, p(2) should be 0 if p(x) is a multiple of g(x)

Thus,

p(2)=2

3

−5(2)

2

+4(2)−3

=8−20+8−3

=−7

=8−20+8−3



=0

Thus, p(x) is not a multiple of g(x)

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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