Factorise: a³ + a² + a + 1

Solution:

Factorization of an algebraic expression refers to finding out the factors of the given algebraic expression.

Given a³ + a² + a + 1

This expression does not have a common factor in all the terms.

Rearranging the terms, we can write it as,

a³ + a² + a + 1 = a²(a + 1) + a + 1

= a²(a + 1) + 1(a + 1)

= (a² + 1) (a + 1)

✦ Try This: Factorise: x⁵ + x⁴ + x³ + x²

Given, x⁵ + x⁴ + x³ + x²

= x⁴(x + 1) + x²(x + 1)

= (x⁴ + x²) (x + 1)

= x²² + 1) (x + 1)

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 9

NCERT Exemplar Class 8 Maths Chapter 7 Problem 88(xi)

Factorise: a³ + a² + a + 1

Summary:

Factorising a³ + a² + a + 1 we get (a² + 1) (a + 1)

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