Question

8. Show that (3x+5) is a factor of 3x3 + 5x2 - 9x - 15. Hence completely factorise the above expression.​

Answer 1

Correct Question :-

Show that (3x + 5) is a factor of 3x³ + 5x² - 9x - 15. Hence completely factorise the above expression.

Required Answer :-

${\sf{:\implies 3x + 5}}$

${\sf{:\implies {x} = - \dfrac{5}{3} }}$

And ,

${\sf{:\implies f( x) \: =3x^{3} + 5x ^{2} - 9x - 15 }}$

★ ( f(-5/3)=0 )

by putting the value of x = -5/3

${\sf{:\implies 3( - \dfrac{5}{3} )^{3} + 5( - \dfrac{5}{3} )^{2} - 9( - \dfrac{5}{3} ) - 15 }}$

${\sf{:\implies \cancel{3}( - \dfrac{5}{ \cancel{3}} )^{3} + 5( - \dfrac{5}{3} )^{2} - \cancel{9}( - \dfrac{5}{ \cancel{3}} ) - 15 }}$

${\sf{:\implies - \dfrac{125}{9} + \dfrac{125}{9} + {15} - 15 }}$

${\sf{:\implies \cancel{ - \dfrac{125}{9}} \cancel{ + \dfrac{125}{9}} \cancel{ + {15}} \cancel { - 15 }} }$

${\sf{:\implies \bold{0}} }$

Hence , (3x + 5) is a factor of 3x³ + 5x² - 9x - 15.