Question

If a polynomial p(x)=x2-4 is divided by a linear polynomial (x-2) the reminder is

Answer 1

Remainder is 0
When we divide x2-4 by x-2

Answer 2

The remainder when the polynomial p(x) = x² - 4 is divided by a linear polynomial x - 2 is 0

Given :

The polynomial p(x) = x² - 4 is divided by a linear polynomial x - 2

To find :

The remainder

Solution :

Step 1 of 3 :

Write down the given polynomials

Here it is given that the polynomial p(x) = x² - 4 is divided by a linear polynomial x - 2

p(x) = x² - 4

Let g(x) = x - 2

Step 2 of 3 :

Find zero of g(x)

For Zero of g(x) we have

g(x) = 0

⇒ x - 2 = 0

⇒ x = 2

∴ Zero of g(x) is 2

Step 3 of 3 :

Find the remainder

By Remainder Theorem the required Remainder when p(x) is g(x) is

$\sf = p(2)$

$\sf = {( 2)}^{2} - 4$

$\sf = 4 - 4$

$\sf = 0$

Hence the polynomial p(x) = x² - 4 is divided by a linear polynomial x - 2 is 0

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