Question

factorise after taking out HCF 5a^3-30a^2+45a​

Answer 1

Factorization

Answer: on factorizing 5a³ - 30a² + 45a we get (5a) ( a²- 6a + 9) .

Explanation:

given expression is as follows

5a³ - 30a² + 45a

Need to Factorize after taking out H.C.F

Here taking out HCF means find the Highest common factor between the three terms of expression and then taking it as common.

lets factorize each term separately  first to determine HCF.

5a³ =   5 x a x a

30a² = 2 x 3 x 5 x a x a

45a =  3 x 3 x 5 x a

so in three terms 5 x a is common , hence H.C.F of three terms is 5 x a , that is 5a

now take 5a common from each term and rewrite the complete expression that is 5a³ can be written as 5a × a² , 30a² can be written as 5a x 6a and 45a can be written as 5a × 9

=> 5a³ - 30a² + 45a = ( 5a × a² - 5a x 6a  +  5a × 9)

As 5a is Highest common factor in all terms , it can be taken out of the bracket.

=> 5a³ - 30a² + 45a = 5a( a² -6a + 9)

Hence on factorizing 5a³ - 30a² + 45a we get (5a) ( a²- 6a + 9 ) .

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