According to the synthetic division below, which of the following statements are true? Check all that apply.
_____
-7 ) 2 10 -20
-14 28
_
2 -4 8

A. (x+7) is a factor of 2x^2+10x-20
B. (x-7) is a factor of 2x^2+10x-20
C. When x=7, 2x^2+10x-20=8
D. When x=-7, 2x^2+10x-20=8
E. When (2x^2+10x-20) is divided by (x+7), the remainder is 8
F. When (2x^2+10x-20) is divided by (x-7), the remainder is 8

Please help!

Here are the answers to the given question above.
According to the synthetic division given above, the statements that are true are the following:
A. (x+7) is a factor of 2x^2+10x-20 --x+7=0 becomes x= -7.
D. When x=-7, 2x^2+10x-20=8
E. When (2x^2+10x-20) is divided by (x+7), the remainder is 8 ---- The last number in the bottom right is always the remainder.
Hope these answers help.

Answer Link

AkshayG AkshayG · Answer 2 · 2019-12-20T08:17:53+01:00

When [tex]x = - 7, 2{x^2} + 10x - 20 = 8[/tex] and If [tex]2{x^2} + 10x -20[/tex] is divided by [tex]\left( {x + 7} \right)[/tex], the remainder is 12. Option (D) is correct and option (E) is correct.

Further Explanation:

Explanation:

If division of a polynomial by a binomial result in a remainder of zero means that the binomial is a factor of polynomial.

The synthetic division can be expressed as follows,

[tex]\begin{aligned}- 7\left| \!{\nderline {\,{2\,\,\,\,\,\,\,\,\,\,10\,\,\,\,\,\,\,\,\,\, - 20} \,}} \right.\hfill\\\,\,\,\,\,\,\underline {\,\,\,\,\,\,\,\,\,\, - 14\,\,\,\,\,\,\,\,\,\,\,\,\,\,28} \hfill\\ \,\,\,\,\,\,\,\,2\,\,\,\,\,\,\,\, - 4\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,8 \hfill\\\end{aligned}[/tex]

The last entry of the synthetic division tells us about remainder and the last entry of the synthetic division is [tex]8[/tex]. Therefore, the remainder of the synthetic division is [tex]8[/tex].

When [tex]x = - 7, 2{x^2} + 10x - 20 = 8[/tex] and If [tex]2{x^2} + 10x -20[/tex] is divided by [tex]\left( {x + 7} \right)[/tex], the remainder is 12. Option (D) is correct and option (E) is correct.

Option (A) is not correct.

Option (B) is not correct.

Option (C) is not correct.

Option (F) is not correct.

Learn more:

Learn more about inverse of the functionhttps://brainly.com/question/1632445.
Learn more about range and domain of the function https://brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Synthetic Division

Keywords: division, factor (x+7), remainder 8, statements, true, apply, divided, binomial synthetic division, long division method, coefficients, quotients, remainders, numerator, denominator, polynomial, zeros, degree.