Question

factorize 4x^4 - 5x^2 + 1

Answer 1

ANSWER.

• (2x + 1)(2x - 1)(x + 1)(x - 1)

SOLUTION.

We have to factorise - 4x⁴ - 5x² + 1

Let u = x². So, the expression becomes,

= 4u² - 5u + 1

By splitting the middle term, we get,

= 4u² - 4u - u + 1

Taking terms as common, we get,

= 4u(u - 1) - 1(u - 1)

= (4u - 1)(u - 1)

Now, substitute back u = x², we get,

= (4x² - 1)(x² - 1)

= (2x + 1)(2x - 1)(x + 1)(x - 1)   [a² - b² = (a + b)(a - b)]

Which is our required answer.