Introduction to factorisation — lesson. Mathematics State Board, Class 9.

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Factorisation:

It is the reverse process of multiplication.

Example:

The factors

$x+1$ and

$x+2$ are multiplied as follows to get a quadratic polynomial.

$x+1$

$\cdot$

$x+2$

$=$

$x^2 + x + 2x + 2$

$=$

$x^2 + 3x + 2$

$x^2 + 3x + 2$ is factorised to get the factors

$x+1$ and

$x+2$ .

Ways of factorisation:

There are two ways of factorization

By factoring out the common term.

Example:

Factorise

$ax^2 + bx$ .

Solution:

Here

$x$ is the common term in the polynomial

$ax^2 + bx$ .

Factor out

$x$ from the polynomial

$ax^2 + bx$ .

$ax^2 + bx$

$=$

$x(ax + b)$

The factors of

$ax^2 + bx$ are

$x$ and

$ax + b$ .

By grouping the items in an expression.

Example:

Factorise

$ax + a + bx + b$ .

Solution:

Group the identical terms in the polynomial

$ax + c + bx + b$ .

$ax + a + bx + b$

$=$

$(ax + a) + (bx + b)$

$=$

$a(x + 1) + b(x + 1)$

Factor out the common terms in the above expression.

$ax + a + bx + b$

$=$

$(x + 1)(a + b)$

The factors of

$ax + a + bx + b$ are

$(x + 1)$ and

$(a + b)$ .

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5. Introduction to factorisation

Theory: