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Factorizing of Monomials

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Question

Factorise $x^{3} - 2 x^{2} - x + 2$

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Solution

Step 1: Polynomial
A polynomial is an algebraic expression in which the exponent on any variable is a whole number. Polynomial’s degree is the highest or the greatest power of a variable in a polynomial equation.
A polynomial can be written as the product of its factors having a degree less than or equal to the original polynomial.
The process of factoring is called factorization of polynomials.
Step 2: Factorization of the polynomial $x^{3} - 2 x^{2} - x + 2$
$x^{3} - 2 x^{2} - x + 2 = x^{2} (x - 2) - 1 (x - 2) = (x - 2) (x^{2} - 1) = (x - 2) (x^{2} - 1^{2}) = (x - 2) (x - 1) (x + 1) [∵ a^{2} - b^{2} = (a + b) (a - b)]$
Hence, the factors of the given polynomial $x^{3} - 2 x^{2} - x + 2$ are $(x - 1), (x + 1)$ and $(x - 2)$ .

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Similar questions

$(x + 1)$ is a factor of the polynomial
(a) $x^{3} - 2 x^{2} + x + 2$ (b) $x^{3} + 2 x^{2} + x - 2$
(c) $x^{3} + 2 x^{2} - x - 2$ (d) $x^{3} + 2 x^{2} - x + 2$

Using the FActor theroem, show that:
(i) (x-2) is a factor fo $x^{3} - 2 x^{2} - 9 x + 18$ Hence factories the expression
(ii) (x+5) is a factor of $2 x^{3} + 5 x^{2} - 28 x - 15$ Hence factorise fthe expression $2 x^{3} + 5 x^{2} - 28 x - 18$ completely.
(iii) (3x+2) is a factor fo $3 x^{3} + 2 x^{2} - 3 x - 2.$ Hence factorise the expression
$3 x^{3} + 2 x^{2} - 3 x - 2$ completely

Factorise;

x^{3} - 2 x^{2} - x + 2

Q. Factorise :
(i)

x^{3} - 2 x^{2} - x + 2

(ii)

x^{3} + 13 x^{2} + 32 x + 20

Factorise :
(i) $x^{3}$ −2 $x^{2}$ −x+2
(ii) 2 $y^{3}$ + $y^{2}$ −2y−1

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Factorise x3-2x2-x+2

Factorise $x^{3} - 2 x^{2} - x + 2$