Question

Factorise: xcube+xsquare-4x-4

Answer 1

x³+x²-4x-4
x³+x²-(2+2)x-4
x³+x²-2x-2x-4
x²(x+1)-2(x+1-2)
(x²-2)(x+1)(x-1)

Answer 2

Concept

Finding the factors of an algebraic expression, also known as locating two or more expressions whose product is the given expression, is the act of factorization. Factorization of algebraic expressions is the process of identifying two or more expressions whose product is the given expression. A factor is a number that divides the provided number by itself with no residue. It simply refers to writing a number as the product of two other integers.

Given

the expression is x³ ₊ x² ₋ 4x ₋ 4

Find

we need to factorize the given expression.

Solution

given, x³ ₊ x² ₋ 4x ₋ 4

factorizing the above equation.

x³ ₊ x² ₋ 4x ₋ 4

take out the common terms

=  x²( x ₊ 1) ₋ 4(x ₊ 1)

= (x ₊ 1) (x² ₋ 4)

(x² ₋ 4) is in the form of (a² ₋ b²) = (a₋b)(a₊b)

=  (x ₊ 1) (x² ₋ 2²)

= (x ₊ 1) (x ₋ 2) (x ₊ 2)

Hence after factorizing the given expression we get the factors as

(x ₊ 1) (x ₋ 2) (x ₊ 2)

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