Question

x^16-x^14+x^9+x^7+x
Factorise

only answer me who can solve this sum.​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Concept

Writing a number or other mathematical object as the result of numerous factors—typically smaller or simpler objects of the same kind—is known as factorization or factoring in mathematics. For instance, the polynomial x2 - 4 and the number 15 may both be factored using the formula 3 x 5.

Given

The expression x¹⁶-x¹⁴+x⁹+x⁷+x is given

Find

We have to factorize the given equation

Solution

The steps are as follow:

x¹⁶-x¹⁴+x⁹+x⁷+x

Taking x common from given expression

we get,

x(x¹⁵-x¹³+x⁸+x⁶+1)

= x(x¹⁵+x¹⁴-x¹⁴-x¹³+x⁸+x⁷-x⁷+x⁶+1)

Taking x⁸ and x^(-7) as common

we get,

= x{x⁸(x⁷+x⁶+1)-x⁷(x⁷+x⁶+1)+(x⁷+x⁶+1)}

= x (x⁷+x⁶+1) (x⁸-x⁷+1)

Hence the factor of given expression x¹⁶-x¹⁴+x⁹+x⁷+x will be x, (x⁷+x⁶+1), and (x⁸-x⁷+1)

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