SaiBook.us Algebra

Lesson Example Discussion Quiz: Class Homework

Quiz At Home

Title: Test1

Grade: 8-b Lesson: S1-P1

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	Multiplying polynomials expression: \$(x^3 + 2x^2 − x − 2)(x^3 − x^2 + 3x − 3) \$	A) \$ x^6 + x^4 + 2x^3 - 7x^2 + 6\$ B) \$ x^6 + x^5 + 2x^3 - 7x^2 - 3x + 6\$ C) \$ x^6 + x^5 + 2x^4 - 7x^3 - 3x^2 + 6x\$ D) \$x^5 + 2x^4 - 3x^3 - 5x^2 + 6x - 9\$
2	Let p(x) be a polynomial that is evenly divisible by \$(x−2)^2\$, and let q(x) = p(x) − 5. Find the value of q(2).	A) -25 B) -5 C) 25 D) -3
3	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\$
4	Simplify the expression \$(3x^3 - 2x^2 + x - 4) + (2x^3 + x^2 - 5x + 6) - (x^3 - 3x^2 + 2x - 1)\$.	A) \$3x^3 + 2x^2 + 2x + 3\$ B) \$4x^3 + 2x^2 - 8x + 3\$ C) \$4x^3 + 2x^2 - 2x + 3\$ D) \$4x^3 + 2x^2 - 6x + 3\$
5	Find the sum of the polynomials \$3a^3 + a^2 - 2a + 7\$ and \$4a^3 - a^2 + a - 5\$.	A) \$6a^3 - a + 2\$ B) \$7a^3 - 2a + 9\$ C) \$7a^3 - a + 2\$ D) \$6a^3 - 7a + 2\$
6	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
7	\$ (2x^3 + 5x^2 - 3x + 7)/(x + 2) \$ If \$ax^2 + bx + c\$ represents the Quotient of the expression shown, then what is the value of a - b?	A) 1 B) 3 C) 2 D) 5
8	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
9	If \$(2x^2 - 1/2 x + 3)\$ is multiplied by \$ (3x - 2/3) \$, what is the coefficient of \$x^2\$ in the resulting polynomial?	A) \$ 28/3\$ B) \$ - 17/6\$ C) -2 D) 6
10	Find the quotient and remainder when \$ 2x^4 − 5x^3 + 3x^2 - 2x + 1 \$ is divided by x + 2.	A) \$ 2x^3 - 19x^2 + 21x - 44 \$ and 87 B) \$ 2x^3 - 9x^2 + 21x - 44 \$ and 89 C) \$ 2x^3 - 9x^2 + 21x - 44 \$ and 88 D) \$ 2x^3 - 9x^2 + 21x - 34 \$ and 90

Problem Id

Problem

Options

Multiplying polynomials expression:
\$(x^3 + 2x^2 − x − 2)(x^3 − x^2 + 3x − 3) \$

A) \$ x^6 + x^4 + 2x^3 - 7x^2 + 6\$

B) \$ x^6 + x^5 + 2x^3 - 7x^2 - 3x + 6\$

C) \$ x^6 + x^5 + 2x^4 - 7x^3 - 3x^2 + 6x\$

D) \$x^5 + 2x^4 - 3x^3 - 5x^2 + 6x - 9\$

Let p(x) be a polynomial that is evenly divisible by \$(x−2)^2\$, and let q(x) = p(x) − 5. Find the value of q(2).

A) -25

B) -5

C) 25

D) -3

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\$

Simplify the expression \$(3x^3 - 2x^2 + x - 4) + (2x^3 + x^2 - 5x + 6) - (x^3 - 3x^2 + 2x - 1)\$.

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

B) \$4x^3 + 2x^2 - 8x + 3\$

C) \$4x^3 + 2x^2 - 2x + 3\$

D) \$4x^3 + 2x^2 - 6x + 3\$

Find the sum of the polynomials \$3a^3 + a^2 - 2a + 7\$ and \$4a^3 - a^2 + a - 5\$.

A) \$6a^3 - a + 2\$

B) \$7a^3 - 2a + 9\$

C) \$7a^3 - a + 2\$

D) \$6a^3 - 7a + 2\$

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

\$ (2x^3 + 5x^2 - 3x + 7)/(x + 2) \$
If \$ax^2 + bx + c\$ represents the Quotient of the expression shown, then what is the value of a - b?

A) 1

B) 3

C) 2

D) 5

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

If \$(2x^2 - 1/2 x + 3)\$ is multiplied by \$ (3x - 2/3) \$, what is the coefficient of \$x^2\$ in the resulting polynomial?

A) \$ 28/3\$

B) \$ - 17/6\$

C) -2

D) 6

Find the quotient and remainder when \$ 2x^4 − 5x^3 + 3x^2 - 2x + 1 \$ is divided by x + 2.

A) \$ 2x^3 - 19x^2 + 21x - 44 \$ and 87

B) \$ 2x^3 - 9x^2 + 21x - 44 \$ and 89

C) \$ 2x^3 - 9x^2 + 21x - 44 \$ and 88

D) \$ 2x^3 - 9x^2 + 21x - 34 \$ and 90