When \(x = - 7, 2{x^2} + 10x - 20 = 8\) and If \(2{x^2} + 10x -20\) is divided by \(\left( {x + 7} \right)\), 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,
\(\begin{aligned}- 7\left| \!{
derline {\,{2\,\,\,\,\,\,\,\,\,\,10\,\,\,\,\,\,\,\,\,\, - 20} \,}} \right.\hfill\\\,\,\,\,\,\,\underline {\,\,\,\,\,\,\,\,\,\, - 14\,\,\,\,\,\,\,\,\,\,\,\,\,\,28} \hfill\\ \,\,\,\,\,\,\,\,2\,\,\,\,\,\,\,\, - 4\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,8 \hfill\\\end{aligned}\)
The last entry of the synthetic division tells us about remainder and the last entry of the synthetic division is \(8\). Therefore, the remainder of the synthetic division is \(8\).
When \(x = - 7, 2{x^2} + 10x - 20 = 8\) and If \(2{x^2} + 10x -20\) is divided by \(\left( {x + 7} \right)\), 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.
