Question

Will the following polynomial will be completely divisible by 2x-1


${2x}^{3} +( { - 28x}^{2} ) + 11x + ( - 28) + 3$
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25 point question. ​

Answer 1

Answer:

p(x)= 2x^3+(-28x^2)+11x+(-28)+3

=2x^3-28x^2+11x-28+3

=2x^3-28x^2+11x-25

g(x)=2x-1

2x-1=0

2x=1

x=1/2

p(1/2)=2(1/2)^3-28(1/2)^2+11(1/2)-25

=2(1/8)-28(1/4)+11(1/2)-25

=(1/4)-7+(11/2)-25

=1-28+22-100/4. (taking LCM)

=-105/4

=-26.25 -ans