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

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When and If is divided by , 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,

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

When and If is divided by , 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.

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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.

D

Step-by-step explanation:

10*20=200

200 + 1020= 1220

Works for the first one

20*20=400

400+ 1020=1420

Works for the second one

30*20=600

600+1020=1620

Works for the third one, and all the others one so forth.

You take the number on the left (10, 20, 30, 40, 50, 60, 70) and times it by 20, replacing the x in the equation with the number on the left side of the table. Then you add the number from said equation to result of the multiplication from the first step.