Polynomial Expression

Which are factors of x^2 - 4x - 5? Select two options. A) (x - 5) B) (x - 4) C) (x - 2) D) (x + 1)E) (x + 5)

A) (x - 5) D) (x + 1)E) (x + 5)

Which binomial is a factor of 9x^2 - 64? A) 3x - 8 B) 9x - 32 C) 3x + 32 D) 9x + 8

A) 3x - 8

What is the greatest common factor of the terms in the polynomial 8x^4 - 4x^3 - 18x^2? A) 2x B) 2x^2 C) 4x D) 4x^2

B) 2x^2

What is the cube root of 8x^27? A) 2x^3 B) 2x^9 C) 4x^3 D) 4x^9

B) 2x^9

Which terms could have a greatest common factor of 5m^2n^2? Select two options. A) m^5n^5 B) 5m^4n^3 C) 10m^4n D) 15m^2n^2 E) 24m^3n^4

B) 5m^4n^3 D) 15m^2n^2

Which is true about the polynomial -3xy^2 + 5x^2y? A) It is a binomial with a degree of 2. B) It is a binomial with a degree of 3. C) It is a trinomial with a degree of 2. D) It is a trinomial with a degree of 3.

B) It is a binomial with a degree of 3.

A square with an area of A^2 is enlarged to a square with an area of 25A^2. How was the side of the smaller square changed? A) The side length was increased by 5. B) The side length was multiplied by 5. C) The side length was increased by 10. D) The side length was multiplied by 10.

B) The side length was multiplied by 5.

Which expression is equivalent to 6x^2 - 19x - 55? A) (2x - 11)(3x + 5) B) (2x + 11)(3x - 5) C) (6x - 11)(x + 5) D) (6x + 11)(x - 5)

D) (6x + 11)(x - 5)

Which is a factor of x^2 + 8x - 48? A) (x - 6) B) (x + 4) C) (x - 16) D) (x + 12)

D) (x + 12)

Which is the completely factored form of 12x^3 - 60x^2 + 4x - 20? A) 4(3x^2 - 1)(x - 5) B) 4x(3x^2 + 1)(x - 5) C) 4x(3x^2 - 1)(x + 5) D) 4(3x^2 + 1)(x - 5)

D) 4(3x^2 + 1)(x - 5)

Which monomial is a perfect cube? A) 16x^6 B) 27x^8 C) 32x^12 D) 64x^6

D) 64x^6

What is the sum of the polynomials? (7x^3 - 4x^2) + (2x^3 - 4x^2) A) 5x^3 B) 9x^3 C) 5x^3 - 8x^2 D) 9x^3 - 8x^2

D) 9x^3 - 8x^2

The polynomial 2x^3 − 5x^2 + 4x − 10 is split into two groups, 2x^3 + 4x and −5x^2 − 10. The GCFs of each group is then factored out. What is the common binomial factor between the two groups after their GCFs have been factored out? A)2x + 5 B)2x − 5 C) x^2 − 2 D) x^2 + 2

D) x^2 + 2

The expression y^2 - 10y + 24 has a factor of y - 4. What is another factor of y^2 - 10y + 24? A) y - 20 B) y - 14 C) y - 8 D) y - 6

D) y - 6

What is the factored form of the polynomial? x^2 - 16x + 48 A) (x − 4)(x − 12) B) (x − 6)(x − 8) C) (x + 4)(x + 12) D) (x + 6)(x + 8)

A) (x − 4)(x − 12)

Simplify the expression -2(p + 4)^2 - 3 + 5p. What is the simplified expression in standard form? A) -2p^2 - 11p - 35 B) 2p^2 + 21p + 29 C) -2p^2 + 13p + 13 D) 4p^2 + 37p - 67

A) -2p^2 - 11p - 35

What is the greatest common factor of 8x and 40y? A) 8 B) 8xy C) 320 D) 320xy

A) 8

Which shows one way to determine the factors of 4x^3 + x^2 - 8x - 2 by grouping? A) x^2(4x + 1) - 2(4x + 1) B) x^2(4x - 1) + 2(4x - 1) C) 4x^2(x + 2) - 1(x + 2) D) 4x^2(x - 2) - 1(x - 2)

A) x^2(4x + 1) - 2(4x + 1)

The expression 40x^2 - 65x + 50 represents the sum of the interior angles of a regular pentagon in degrees. If the interior angles of the pentagon are equal, which expression represents the measure of two angles? A) 2x^2(20 - 32x + 25x^2) B) 2(8x^2 - 13x +10) C) 5x^2(8x^2 - 13x + 10) D) 5(3x^2 - 8x + 5)

B) 2(8x^2 - 13x +10)

The revenue, in dollars, of a company that produces jeans can be modeled by 2x^2+17x−175. The cost, in dollars, of producing the jeans can be modeled by 2x^2−3x−125. The number of pairs of jeans that have been sold is represented by x. If the profit is the difference between the revenue and the cost, which expression can be used to find profit and what is that profit when 75 pairs of jeans are sold? A) 20x−50; $500 B) 20x−50; $1,450 C) 20x+50; $1,550 D) 20x+50; $5,250

B) 20x−50; $1,450

Tyrone factored the polynomial completely. What is the value of B? 12x^4 + 30x^3 + 4x^2 + 10x Ax(Bx^2+1)(2x+5) A) 2 B) 3 C) 5 D) 6

B) 3

What is the greatest common factor of the terms in the polynomial 12x^4 + 27x^3 + 6x^2? A) 3x B) 3x^2 C) 6x^2 D) 6x^4

B) 3x^2

Candy draws a square design with a side length of x inches for the window at the pet shop. She takes the design to the printer and asks for a sign that has an area of 16x^2 - 40x + 25 square inches. What is the side length, in inches, of the pet shop sign? A) 4x + 5 B) 4x - 5 C) 8x + 5 D) 8x - 5

B) 4x - 5

Which monomials are perfect squares? Select three options. A) 6x^2 B) 9x^8 C) 16x^9 D) 25x^12 E) 36x^16

B) 9x^8 D) 25x^12 E) 36x^16

Which statement is true about the polynomial 3x^2y^2 − 5xy^2 − 3x^2y^2 + 2x^2 after it has been fully simplified? A) It has 2 terms and a degree of 2. B) It has 2 terms and a degree of 3. C) It has 4 terms and a degree of 2. D) It has 4 terms and a degree of 4.

B) It has 2 terms and a degree of 3.

Which will result in a difference of squares? A) (-7x+4) (-7x+4) B) (-7x+4) (4-7x) C) (-7x-4) (-7x-4) D) (-7x+4) (7x-4)

C) (-7x-4) (-7x-4)

Which is the completely factored form of 4x^2 + 28x + 49? A) (x + 7)(4x + 7) B) 4(x + 7)(x + 7) C) (2x + 7)(2x + 7) D) 2(x + 7)(x + 7)

C) (2x + 7)(2x + 7)

Tomas learned that the product of the polynomials (a + b)(a^2 - ab + b^2) was a special pattern that would result in a sum of cubes, a^3 + b^3. His teacher put four products on the board and asked the class to identify which product would result in a sum of cubes if a = 2x and b = y. Which product should Tomas choose? A) (2x + y)(2x^2 + 2xy - y^2) B) (2x + y)(4x^2 + 2xy - y^2) C) (2x + y)(4x^2 - 2xy + y^2) D) (2x + y)(2x^2 - 2xy + y^2)

C) (2x + y)(4x^2 - 2xy + y^2)

Factor -7x^3 + 21x^2 + 3x - 9 by grouping. What is the resulting expression? A) (3 - 7x)(x^2 - 3) B) (7x - 3)(3 + x^2) C) (3 - 7x^2)(x - 3) D) (7x^2 - 3)(3 + x)

C) (3 - 7x^2)(x - 3)

Factor x^3 - 7x^2 - 5x + 35 by grouping. What is the resulting expression? A) (x^2 - 7)(x - 5) B) (x^2 - 7)(x + 5) C) (x^2 - 5)(x - 7) D) (x^2 + 5)(x - 7)

C) (x^2 - 5)(x - 7)

Zohar is using scissors to cut a rectangle with a length of 5x - 2 and a width of 3x + 1 out of a larger piece of paper. Which expression can be used to find the perimeter of the rectangle and what is the perimeter if x = 4? A) (5x−2)+(3x+1); 31 centimeters B) (5x−2)+(3x+1); 36 centimeters C) 2(5x−2)+2(3x+1); 62 centimeters D) 2(5x−2)+2(3x+1); 70 centimeters

C) 2(5x−2)+2(3x+1); 62 centimeters

Which term completes the product so that it is the difference of squares? (−5x−3)(−5x+________) A) −9 B) −3 C) 3 D) 9

C) 3

A square has a perimeter of 12x + 52 units. Which expression represents the side length of the square in units? A) x + 4 B) x + 40 C) 3x + 13 D) 3x + 43

C) 3x + 13

The revenue, in dollars, of a company that makes toy cars can be modeled by the polynomial 3x^2 + 4x - 60. The cost, in dollars, of producing the toy cars can be modeled by 3x^2 - x + 200. The number of toy cars sold is represented by x. If the profit is the difference between the revenue and the cost, what expression represents the profit? A) 3x - 260 B) 3x + 140 C) 5x - 260 D) 5x + 140

C) 5x - 260

What is the product of (2p + 7)(3p^2 + 4p - 3)? A) 6p^3 + 29p^2 - 34p + 21 B) 6p^3 + 29p^2 - 22p + 21 C) 6p^3 + 29p^2 + 22p - 21 D) 6p^3 + 29p^2 + 34p - 21

C) 6p^3 + 29p^2 + 22p - 21

What is the difference of the polynomials? (8r^6s^3 - 9r^5s^4 + 3r^4s^5) - (2r^4s^5 - 5r^3s^6 - 4r^5s^4) A) 6r^6s^3 - 4r^5s^4 + 7r^4s^5 B) 6r^6s^3 - 13r^5s^4 - r^4s^5 C) 8r^6s^3 - 5r^5s^4 + r^4s^5 + 5r^3s^6 D) 8r^6s^3 - 13r^5s^4 + r^4s^5 - 5r^3s^6

C) 8r^6s^3 - 5r^5s^4 + r^4s^5 + 5r^3s^6