Perform the indicated division.
A) x - 27
B) x + 31
C) x - 28
D) x + 28
E) x + 25

Question

Perform the indicated division. 
A) x - 27 
B) x + 31 
C) x - 28 
D) x + 28 
E) x + 25

Quizplus · Accepted Answer

This is a polynomial long division problem. The divisor is x - 28. The first term of the quotient is obtained by dividing the first term of the dividend by the first term of the divisor:

11ec1 ÷ x = 11ec1x⁰ = 11ec1

The first term of the dividend 11ec1x⁴ has four more powers of x than the divisor x - 28, so we multiply the divisor by x⁴:

x⁴(x - 28) = x⁵ - 28x⁴

We subtract this from the dividend:

11ec1x⁴ - (x⁵ - 28x⁴) = x⁵ - 11ec1x⁴

The next term of the quotient is obtained by dividing the first term of what's left of the dividend by the first term of the divisor:

x⁵ ÷ x = x⁴

We multiply the divisor by x⁴ and subtract:

x⁴(x - 28) = x⁵ - 28x⁴

(x⁵ - 11ec1x⁴) - (x⁵ - 28x⁴) = 1676x⁴

The next term of the quotient is obtained by dividing the first term of what's left of the dividend by the first term of the divisor:

1676x⁴ ÷ x = 1676x³

We multiply the divisor by 1676x³ and subtract:

1676x³(x - 28) = 1676x⁴ - 47a48x³

(1676x⁴ - 47a48x³) - (1676x⁴ - 28x³) = 47d0x³

We repeat this process until there's nothing left to divide:

47d0x³ ÷ x = 47d0x²
47d0x²(x - 28) = 47d0x³ - cbec0x²
(47d0x³ - cbec0x²) - (47d0x³ - 28x²) = cb941x²
cb941x² ÷ x = cb941x
cb941x(x - 28) = cb941x² - 1edfc8x
(cb941x² - 1edfc8x) - (cb941x² - 28x) = 66618x
66618x ÷ x = 66618
66618(x - 28) = 66618x - 1243b8
(66618x - 1243b8) - (66618x - 28x) = 124390

The remainder is 124390. Therefore, the answer is D, x + 28, because that's the divisor.

Perform the Indicated Division