Advertisements
Advertisements
Question
Factorize: x4 + x2 + 25.
Solution
The given expression to be factorized is x4 + x2 + 25
This can be written in the form
x4 + x2 + 25= ` (x^2)^2 + 2x^2 .5 + (5)^2 - 9x^2`
` = {(x^2)^2 + 2x^2 .5 + (5)^2}- (3x)^2`
` = (x^2 + 5)^2 - (3x)^2`
` = (x^2 + 5 + 3x) (x^2 + 5 - 3x)`
We cannot further factorize the expression.
So, the required factorization is. `x^4 + x^2 + 25 = (x^2 + 5+3x)(x^2 + 5 - 3x)`
APPEARS IN
RELATED QUESTIONS
Get the algebraic expression in the following case using variables, constants and arithmetic operations.
One-fourth of the product of numbers p and q.
Factorize: x3 + x - 3x2 - 3
Factorize a2 + 2ab + b2 - c2
Factorize `x^2 - sqrt3x - 6`
Factorize the following expressions:
10x4y – 10xy4
Factorize the following expressions:
( x + 2)3 + ( x - 2)3
(3x - 2 y)3 + (2 y - 4z )3 + (4z - 3x)3
Express the following as an algebraic expression:
The product of 12, x, y and z minus the product of 5, m and n.
Find the average (A) of four quantities p, q, r and s. If A = 6, p = 3, q = 5 and r = 7; find the value of s.
Write the coefficient of x2 and x in the following polynomials
`sqrt(3)x^2 + sqrt(2)x + 0.5`
