Question

Q:-one of the factor of(x-b)^5+(b-a)^5 is
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Answer 1

One of the factor of (x - b)⁵ + (b - a)⁵ is x - a

Given :

The expression (x - b)⁵ + (b - a)⁵

To find :

Find One of the factor of (x - b)⁵ + (b - a)⁵

Solution :

Step 1 of 2 :

Find zero of the polynomial

Let f(x) be the given polynomial

Then f(x) = (x - b)⁵ + (b - a)⁵

Now we have

$\sf f( a) = {( a - b)}^{5} + {(b - a)}^{5}$

$\sf \implies \: f( a) = {( a - b)}^{5} - {(a - b)}^{5}$

$\sf \implies \: f( a) = 0$

So x = a is one of the zeros of the polynomial

Step 2 of 2 :

Find One of the factor

Since x = a is one of the zeros of the polynomial

So by Factor Theorem x - a is one factor of (x - b)⁵ + (b - a)⁵

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