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Lesson Example Discussion Quiz: Class Homework

Quiz In Class

Title: Polynomial functions

Grade: 1400-a Lesson: S2-L2

Explanation: Hello Students, time to practice and review. Let us take next 10-15 minutes to solve the ten 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: in Class

Problem Id	Problem	Options
1	Which of the following could be the graph of \$y = ax^3 + bx^2 + cx + 2\$ where a, b and c are real numbers?	A) $1.1$ B) $1.2$ C) $1.3$ D) $1.4$
2	Which of the following could be the graph of \$y = -2x^5 + p(x)\$, where p(x) is a fourth degree polynomial?	A) $2.1$ B) $2.2$ C) $2.3$ D) $2.4$
3	Which of the following could be the graph of \$y = k(x - 2 )^m (x + 1)^n\$, where k is a real number, m is an even integer, and n is an odd integer?	A) $3.1$ B) $3.2$ C) $3.3$ D) $3.4$
4	The HCF and LCM of two polynomials, are 3x + 1 and \$30x^3 + 7x^2 -10x - 3\$ respectively. If one polynomial is \$6x^2 + 5x + 1\$, then what is the other polynomial?	A) \$15x^2 + 4x + 3\$ B) \$15x^2 + 4x - 3\$ C) None of the above. D) \$15x^2 - 4x - 3\$
5	If 4 is Zero of \$f(x) = 3x^3 + kx - 8\$, what is k?	A) - 50 B) - 48 C) - 46 D) - 52
6	Factor each of the polynomials \$6x^4+ 17x^3+ 25x^2+ 34x - 40\$.	A) \$(8x+3)(x−2)(x^2+2+9)\$ B) \$(1x+1)(3x-1)(x^4+x+1)\$ C) \$(2x+5)(3x−2)(x^2+x+4)\$ D) \$(2x+5)(3x−2)(x^3+4+x)\$
7	Solve each of the inequalities \$x^6 - 4x^4 - 16x^2 + 64 ≥ 0\$.	A) \$ x ∈ (-∞, -2) ∪ (2,∞)\$ B) \$ x ∈ (-∞, -1) ∪ (1,∞)\$ C) \$ x ∈ (-∞, -2) \$ D) \$ x ∈ (2,∞)\$
8	Find roots of a polynomial: Solve \$x^3 - 3x^2 - 4x + 12 = 0\$ for its roots.	A) x = 2, 3, − 2 B) x = 4, 5, − 2 C) x = 2, 6, − 2 D) x = 10, 3, − 2
9	Apply the Remainder Theorem: Determine if x−3 is a factor of q(x)= \$2x^4 - 5x^3 + 3x^2 −7x + 6\$.	A) q(3) ≠ 1 B) q(3) ≠ 0 C) q(3) ≠ 2 D) q(3) = 0
10	Solve each of the equations \$x^6 - 4x^4 -16x^2 + 64 = 0\$.	A) \$x = ± 1 "or" x = ± 1"i"\$ B) \$x = ± 2 "or" x = ± 2"i"\$ C) \$x = ± 6 "or" x = ± 2"i"\$ D) \$x = ± 2 "or" x = ± 5"i"\$

Problem Id

Problem

Options

Which of the following could be the graph of \$y = ax^3 + bx^2 + cx + 2\$ where a, b and c are real numbers?

A) $1.1$

B) $1.2$

C) $1.3$

D) $1.4$

Which of the following could be the graph of \$y = -2x^5 + p(x)\$, where p(x) is a fourth degree polynomial?

A) $2.1$

B) $2.2$

C) $2.3$

D) $2.4$

Which of the following could be the graph of \$y = k(x - 2 )^m (x + 1)^n\$, where k is a real number, m is an even integer, and n is an odd integer?

A) $3.1$

B) $3.2$

C) $3.3$

D) $3.4$

The HCF and LCM of two polynomials, are 3x + 1 and \$30x^3 + 7x^2 -10x - 3\$ respectively. If one polynomial is \$6x^2 + 5x + 1\$, then what is the other polynomial?

A) \$15x^2 + 4x + 3\$

B) \$15x^2 + 4x - 3\$

C) None of the above.

D) \$15x^2 - 4x - 3\$

If 4 is Zero of \$f(x) = 3x^3 + kx - 8\$, what is k?

A) - 50

B) - 48

C) - 46

D) - 52

Factor each of the polynomials \$6x^4+ 17x^3+ 25x^2+ 34x - 40\$.

A) \$(8x+3)(x−2)(x^2+2+9)\$

B) \$(1x+1)(3x-1)(x^4+x+1)\$

C) \$(2x+5)(3x−2)(x^2+x+4)\$

D) \$(2x+5)(3x−2)(x^3+4+x)\$

Solve each of the inequalities \$x^6 - 4x^4 - 16x^2 + 64 ≥ 0\$.

A) \$ x ∈ (-∞, -2) ∪ (2,∞)\$

B) \$ x ∈ (-∞, -1) ∪ (1,∞)\$

C) \$ x ∈ (-∞, -2) \$

D) \$ x ∈ (2,∞)\$

Find roots of a polynomial: Solve \$x^3 - 3x^2 - 4x + 12 = 0\$ for its roots.

A) x = 2, 3, − 2

B) x = 4, 5, − 2

C) x = 2, 6, − 2

D) x = 10, 3, − 2

Apply the Remainder Theorem: Determine if x−3 is a factor of q(x)= \$2x^4 - 5x^3 + 3x^2 −7x + 6\$.

A) q(3) ≠ 1

B) q(3) ≠ 0

C) q(3) ≠ 2

D) q(3) = 0

Solve each of the equations

\$x^6 - 4x^4 -16x^2 + 64 = 0\$.

A) \$x = ± 1 "or" x = ± 1"i"\$

B) \$x = ± 2 "or" x = ± 2"i"\$

C) \$x = ± 6 "or" x = ± 2"i"\$

D) \$x = ± 2 "or" x = ± 5"i"\$