According to synthetic division following statements are true ,
A. When [tex](2x^{2} +9x-7)[/tex] divided by (x+6) , the remainder is 11.
E. When x = -6 , [tex](2x^{2} +9x-7) = 11[/tex] .
What is synthetic division?
" Synthetic division is defined as to simplify a division of highest degree polynomial by lowest degree polynomial."
According to the question,
A. When [tex](2x^{2} +9x-7)[/tex] divided by (x+6) , the remainder is 11.
As shown in the attached file of Synthetic division.
Option A is correct statement.
B. When [tex](2x^{2} +9x-7)[/tex] divided by (x-6) , the remainder is 11.
As shown in the attached file of Synthetic division , the remainder is 119.
Option B is not a correct statement.
C. (x-6) is a factor of [tex](2x^{2} +9x-7)[/tex].
As shown in the attached file of Synthetic division , the remainder is 119.
(x-6) is not a factor of [tex](2x^{2} +9x-7)[/tex]
Option C is not a correct statement.
D. (x+6) is a factor of [tex](2x^{2} +9x-7)[/tex].
As shown in the attached file of Synthetic division , the remainder is 11.
(x+6) is not a factor of [tex](2x^{2} +9x-7)[/tex].
Option D is not a correct statement.
E. When x = -6 [tex](2x^{2} +9x-7) = 11[/tex] .
[tex]2(-6^{2}) +9(-6) -7\\\\= 72-54-7\\\\=11[/tex]
Option E is a correct statement.
F. When x = 6 [tex](2x^{2} +9x-7) = 11[/tex] .
[tex]2(6^{2}) +9(6) -7\\\\= 72+54-7\\\\=119[/tex]
Option F is not a correct statement.
Hence , Option A and Option E are true statement.
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