Question

According to the synthetic division below, which of the following statements are true?

Answer 1

Answer:

Correct options are A and D

Step-by-step explanation:

According to the synthetic division in the diagram you can write down the result of division:

$2x^2+9x-7=(x-(-6))(2x-3)+11,\\ \\2x^2+9x-7=(x+6)(2x-3)+11.$

Therefore,

• when $2x^2+9x-7$ is divided by $x+6,$ the remainder is 11 (option D is correct). To find the remainder after division by $x-6,$ you have to use another synthetic division. Actually, $2x^+9x-7=(x-6)(2x+21)+119,$ then the remainder is 119 (option C is false).
• when $x=-6,$ the expression $x+6$ is $-6+6=0$ and $2x^2+9x-7=0\cdot (2x-3)+11=11$ (option A is correct). You cannot state the same when $x=6$ (option B is false).
• neither $x-6$ nor $x+6$ is a factor of $2x^2+9x-7,$ because the remainders in both cases are not equal to 0 (options E and F are false).

Answer 2

When $x= - 6,2{x^2} + 9x -7= 11$ and when $2{x^2} + 9x -7$ is divided by $\left( {x + 6} \right)$, the remainder is 11.Option (A) is correct and option (D) is correct.

Further Explanation:

Given:

Explanation:

The synthetic division can be expressed as follows,

$\begin{aligned}- 6\left| \!{\nderline {\,{2\,\,\,\,\,\,\,\,\,\,9\,\,\,\,\,\,\,\,\,\,\, - 7} \,}} \right. \hfill\\\,\,\,\,\,\,\underline {\,\,\,\,\,\,\,\, - 12\,\,\,\,\,\,\,\,\,\,\,\,18} \hfill\\\,\,\,\,\,\,\,\,2\,\,\,\,\,\, - 3\,\,\,\,\,\,\,\,\,\,\,\,11 \hfill \\\end{aligned}$

The last entry of the synthetic division tells us about remainder and the last entry of the synthetic division is 11. Therefore, the remainder of the synthetic division is 11.

When $x= - 6, 2{x^2} + 9x -7= 11$ and when $2{x^2} + 9x -7$ is divided by $\left( {x + 6} \right)$, the remainder is 11. Option (A) is correct and option (D) is correct.

Learn more:

1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.
2. Learn more about equation of circle brainly.com/question/1506955.
3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Synthetic Division

Keywords: division, factor (x+5), remainder 12, statements, true, apply, divided, binomial synthetic division, long division method, coefficients, quotients, remainders, numerator, denominator, polynomial, zeros, degree.