Solution: Write the dividend in the coefficient form, and write -3 to the left of the 1st coefficient

FACTORING :

Factor : When a number or an expression is the product of two or more numbers or expressions, each of the latter is called a factor of the former. Thus 4 and 7 are factors of 28 and ( x + y ) and ( x - y ) are factors of x² - y².

Factoring or factorization is the process of changing any algebraic or numerical expression from a sum of terms into a product of factors. A number or expression is said to be prime if no factors can be obtained of that.

We have seen that x ( a + b + c ) = x a + x b + x c.

(1) shows that x and ( a + b + c ) are factors x a + x b + x c .

Here we notice that every term on L. H. S. of (1) contains x as a factor. The other factor ( a + b + c ) can be obtained by dividing the given expression x a + x b + x c by the common factor x .

Example Factorise 5x³ + 7x

Solution: 5x³ + 7x = x (5x² + 7 )

Example Find the factor of ap - aq + a r

Solution: ap - aq + a r = a ( p - q + r )

Example Factorise 2m³ + 8m² + 10m

Solution: 2m³ + 8m² + 10m = 2m ( m² + 4m + 10 )

Example Find the factors of 2a³b - 8a²b²

Solution: 2a³b - 8a² b² = 2a² b ( a - 2b )

Example Factorise c ( a + b ) + d ( a + b ) + e ( a + b )

Solution: c ( a + b ) + d ( a + b ) + e ( a + b ) = ( a + b ) ( c                + d + e )

2. Factors by arranging terms in suitable groups.

Example Factorise ac + bc + bd + ad + ae + be

Solution: Here we cannot find a common factor. We can form suitable groups, thus expression

or expression

Example Resolve into factors x³ + 2x²y - 2xy² - 4y³

Solution: x³ + 2x²y - 2xy² - 4y³ =

Example ax - ay - bx + by + cx - cy