Question

show that
a.) ( 2x-3) is a factor of x + 2x cube - 9x square + 12 .
b.) (x + 3) is a factor of 69 + 11x - x square + x cube
please solve these questions​

Answer 1

Step-by-step explanation:

[A] 2x-3=0

2x=3

x=3/2

(^3;^2 is cube , square for your understanding)

x+2x^3 - 9x^2+12

now u have to arrange them in order:

=2x^3 - 9x^2 +x +12

now substitute x=3/2

=2*{3/2}^3 -9*{3/2}^2 + 3/2 +12 ( * multiply symbol)

now cancel the no.s and u will have

=27/4 - 9*9/4 +3/2 +12

now take LCM

27-81+6+48 divide by 4 on whole

so= -54+54/4

= 0/4 = 0

therefore it is an factor.

[B] x+3=0

x= -3

69 + 11x - x^2 + x^3

now arrange them:

x^3 - x^2 +11x +69

now substitute x= -3

=(-3)^3 -(-3)^2 +11(-3)+69

= -27-9-33+69

= -69+69

=0

therefore it in an factor

[I hope this helped you :) ]