Question

factorise the following fast please
x³ – 5x² + x - 5
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Answer 1

Following are the steps for getting the answer :

Given:

x³ – 5x² + x - 5

To find:

Factor of x³ – 5x² + x - 5

Solution:

we will factorize the given expression

= x³ - 5x² +x – 5

take a x² from  x³ - 5x² and 1 from +x – 5

=x²(x-5)+1(x-5)

take a common (x-5)

now ,

=(x-5)(x²+1)

hence, the factor of  x³ – 5x² + x - 5 is (x-5)(x²+1)

Answer 2

Answer:

Factoring the given equation, we get

$x^{3}-5x^{2}+x-5=(x^{2}+1)(x-5)$.

Step-by-step explanation:

Given equation is $x^{3}-5x^{2}+x-5$.

We have to factorize the given equation.

Factorization or factoring consists of writing a number or another mathematical object as a product of several factors.

Rewrite the equation as

$x^{3}+x-5x^{2}-5$

Now take $x$ as common from the terms $x^{3},x$ and $-5$ as common from the terms $-5x^{2},-5$, we get

$x(x^{2}+1)-5(x^{2}+1)$

Now taking $x^{2} +1$ as common, we get

$(x^{2} +1)(x-5)$

We cannot simplify the equation $x^{2} +1$ further.

So the equation after factorization is

$x^{3}-5x^{2}+x-5=(x^{2}+1)(x-5)$.