Question

Factorise:- x^4-11x^2+10​

Answer 1

Answer:

Question :-

➪ x⁴ - 11x² + 10

Formula used:-

➪ a² - b²

➭ (a + b) (a - b)

Solution :-

➪ x⁴ - 11x² + 10

➭ x⁴ - 10x² - x² + 10

➭ x²(x² - 10) - 1(x² - 10)

➭ (x² - 10) (x² - 1)

➭ (x² - 10) {(x)² - (1)²}

➭ (x² - 10) (x + 1) (x - 1)

∴ The value of x⁴ - 11x² + 10 is

(x²- 10) (x + 1) (x - 1)

Answer 2

Given:

The expression is

${x}^{4} - 11 {x}^{2} + 10$

To find:

We have to factorise it.

Solution:

To determine the factors of the above expression we have to follow the below steps as follows-

The expression is

${x}^{4} - 11 {x}^{2} + 10$

The number 10 can be written as a multiple of 10 and 1 whose sum is equal to 11.

Hence we can write-

${x}^{4} - 11 {x}^{2} + 10 \\ {x}^{4} - 10 {x}^{2} - {x}^{2} + 10 \\ {x}^{2} ( {x}^{2} - 10) - 1( {x}^{2} - 10) \\ ( {x}^{2} - 10)( {x}^{2} - 1) \\ ( {x}^{2} - 10)(x + 1)(x - 1)$

The factors of the above expression are $( {x}^{2} - 10)(x + 1)(x - 1)$.