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Lesson Example Discussion Quiz: Class Homework

Quiz At Home

Title: Synthetic division

Grade: 8-a Lesson: S1-L4

Explanation: Hello Students, time to practice and review. Let us take next 10-15 minutes to solve the five problems using the Quiz Sheet. Then submit the quiz to get the score. This is a good exercise to check your understanding of the concepts.

Quiz: at Home

Problem Id	Problem	Options
1	Perform the synthetic division \$ 4x^4 + 3x^3 - 2x^2 - 7x + 5 \$ by \$ x + 3 \$, and find the quotient and remainder.	A) Quotient = \$ 2x^3 - 9x^2 + 25x - 82 \$, Remainder = 249 B) Quotient = \$ 4x^3 - 7x^2 + 25x - 82 \$, Remainder = 250 C) Quotient = \$ 4x^3 - 9x^2 + 25x - 82 \$, Remainder = 251 D) Quotient = \$ 4x^3 - 9x^2 + 25x - 62 \$, Remainder = 252
2	Divide the polynomial \$ x^5 - 2x^3 + 5x^2 + 7x - 1\$ by the binomial (x + 4).	A) \$ x^4 - 4x^3 + 14x^2 - 51x + 211 - ( 145/( x + 4 )) \$ B) \$ x^4 - 2x^3 + 14x^2 - 51x + 211 - ( 845/( x + 4 )) \$ C) \$ x^4 - 4x^3 + 14x^2 - 31x + 211 - ( 845/( x + 4 )) \$ D) \$ x^4 - 4x^3 + 14x^2 - 51x + 211 - ( 845/( x + 4 )) \$
3	Perform synthetic division to divide \$ 2x^3 - 5x^2 − 3x + 9 \$ by \$ x − 3 \$.	A) \$ 2x^2 + 5x + (9/(x-3)) \$ B) \$ 2x^2 + x + (9/(x-3)) \$ C) \$ 2x^2 + x + (7/(x-3)) \$ D) \$ 3x^2 + x + (9/(x-3)) \$
4	Using synthetic division, determine the remainder when the polynomial \$ x^4 − 2x^3 + 4x^2 - 3x + 6 \$ is divided by the binomial \$ x + 5 \$.	A) 996 B) 999 C) 997 D) 998
5	Perform synthetic division to solve the following expression: \$ ( 7x^3 - 5x^2 - 2x + 3 )/( x - 4 ) \$, find the quotient.	A)\$ 7x^2 + 23x + 90 \$ B) \$ 5x^2 + 29x + 90 \$ C) \$ 7x^2 + 23x + 70 \$ D) \$ 5x^2 + 23x + 90 \$
6	Perform synthetic division to solve the following expression: \$ (6x^2 - 13x + 20)/(x - 3) \$.	A) \$ (6x + 5 + 35)/(x - 3) \$ B) \$ (6x + 5 + 35)/(x - 3) \$ C) \$ (6x - 5 + 165)/(x - 3) \$ D) \$ (13x - 20 + 165)/(x + 3) \$
7	Using synthetic division, determine the remainder when the polynomial \$ x^4 + 3x^3 - 7x^2 + 5x - 2 \$ is divided by the binomial \$x + 1\$.	A) 24 B) 16 C) 39 D) 45
8	Divide the polynomial \$ x^6 - x^5 + x^2 + 2 \$ by the binomial \$ x - 1 \$.	A) Quotient = \$ x^5 + x^4 + 1 \$ with Remainder = 1 B) Quotient = \$ x^4 + 2x - 1 \$ with Remainder = 2 C) Quotient = \$ x^5 + x + 1 \$ with Remainder = 3 D) Quotient = \$ 2x^5 - 5x + 1 \$ with Remainder = 7
9	Divide the following polynomial using synthetic division \$ (5x^5 - 20x^4 - x^2 + 14x - 40) \div (x - 4)\$.	A) \$ (5x^4 - x^3 + 10x + 3)/(x - 4)\$ B) \$ (5x^4 - x^2 + 10x + 22)/(x - 4) \$ C) \$ 5x^4 - x + 10\$ D) \$ 5x^4 + x - 10\$
10	Perform the synthetic division \$x^4 + 2x^3 - 10x^2 - 14x + 8\$ by \$x + 1\$, and find the quotient.	A) \$ x^3 + 2x^2 + 11x - 3\$ B) \$ x^3 + 2x^2 - 12x - 4\$ C) \$ x^3 - x^2 - 11x + 3\$ D) \$ x^3 + x^2 - 11x - 3\$

Problem Id

Problem

Options

Perform the synthetic division \$ 4x^4 + 3x^3 - 2x^2 - 7x + 5 \$ by \$ x + 3 \$, and find the quotient and remainder.

A) Quotient = \$ 2x^3 - 9x^2 + 25x - 82 \$,
Remainder = 249

B) Quotient = \$ 4x^3 - 7x^2 + 25x - 82 \$,
Remainder = 250

C) Quotient = \$ 4x^3 - 9x^2 + 25x - 82 \$,
Remainder = 251

D) Quotient = \$ 4x^3 - 9x^2 + 25x - 62 \$,
Remainder = 252

Divide the polynomial \$ x^5 - 2x^3 + 5x^2 + 7x - 1\$ by the binomial (x + 4).

A) \$ x^4 - 4x^3 + 14x^2 - 51x + 211 - ( 145/( x + 4 )) \$

B) \$ x^4 - 2x^3 + 14x^2 - 51x + 211 - ( 845/( x + 4 )) \$

C) \$ x^4 - 4x^3 + 14x^2 - 31x + 211 - ( 845/( x + 4 )) \$

D) \$ x^4 - 4x^3 + 14x^2 - 51x + 211 - ( 845/( x + 4 )) \$

Perform synthetic division to divide \$ 2x^3 - 5x^2 − 3x + 9 \$ by \$ x − 3 \$.

A) \$ 2x^2 + 5x + (9/(x-3)) \$

B) \$ 2x^2 + x + (9/(x-3)) \$

C) \$ 2x^2 + x + (7/(x-3)) \$

D) \$ 3x^2 + x + (9/(x-3)) \$

Using synthetic division, determine the remainder when the polynomial \$ x^4 − 2x^3 + 4x^2 - 3x + 6 \$ is divided by the binomial \$ x + 5 \$.

A) 996

B) 999

C) 997

D) 998

Perform synthetic division to solve the following expression: \$ ( 7x^3 - 5x^2 - 2x + 3 )/( x - 4 ) \$, find the quotient.

A)\$ 7x^2 + 23x + 90 \$

B) \$ 5x^2 + 29x + 90 \$

C) \$ 7x^2 + 23x + 70 \$

D) \$ 5x^2 + 23x + 90 \$

Perform synthetic division to solve the following expression: \$ (6x^2 - 13x + 20)/(x - 3) \$.

A) \$ (6x + 5 + 35)/(x - 3) \$

B) \$ (6x + 5 + 35)/(x - 3) \$

C) \$ (6x - 5 + 165)/(x - 3) \$

D) \$ (13x - 20 + 165)/(x + 3) \$

Using synthetic division, determine the remainder when the polynomial \$ x^4 + 3x^3 - 7x^2 + 5x - 2 \$ is divided by the binomial \$x + 1\$.

A) 24

B) 16

C) 39

D) 45

Divide the polynomial \$ x^6 - x^5 + x^2 + 2 \$ by the binomial \$ x - 1 \$.

A) Quotient = \$ x^5 + x^4 + 1 \$ with Remainder = 1

B) Quotient = \$ x^4 + 2x - 1 \$ with Remainder = 2

C) Quotient = \$ x^5 + x + 1 \$ with Remainder = 3

D) Quotient = \$ 2x^5 - 5x + 1 \$ with Remainder = 7

Divide the following polynomial using synthetic division \$ (5x^5 - 20x^4 - x^2 + 14x - 40) \div (x - 4)\$.

A) \$ (5x^4 - x^3 + 10x + 3)/(x - 4)\$

B) \$ (5x^4 - x^2 + 10x + 22)/(x - 4) \$

C) \$ 5x^4 - x + 10\$

D) \$ 5x^4 + x - 10\$

Perform the synthetic division \$x^4 + 2x^3 - 10x^2 - 14x + 8\$ by \$x + 1\$, and find the quotient.

A) \$ x^3 + 2x^2 + 11x - 3\$

B) \$ x^3 + 2x^2 - 12x - 4\$

C) \$ x^3 - x^2 - 11x + 3\$

D) \$ x^3 + x^2 - 11x - 3\$