ranjot0143
Answered

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Factorise 9a³ - 27a² - 100a + 300, if it is given that (3a + 10) is a factor of it.​

Sagot :

Answer:

(3a + 10)(3a - 10(a - 3).

Step-by-step explanation:

Do a long division:

3a + 10 ) 9a^3 - 27a^2 - 100a + 300 ( 3a^2 - 19a + 30 <----- Quotient

              9a^3 + 30a^2

                        -57a^2 - 100a

                        -57a^2 - 190a

                                       90a + 300

                                       90a + 300

                                        ..................

Factorise the Quotient:

3a^2 - 19a + 30

= 3a^2 - 9a - 10a + 30

= 3a(a - 3) - 10(a - 3)

= (3a - 10)(a - 3)

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