Quiz about Unit 9: Polynomials

Question 1

Identify the factors of the given polynomial equation: y = $$4x^2(3x - 2)$$ .

Accepted Answer

$$4x^2\ and\ (3x-2)$$

Answer

$$4x\ and\ (3x-2)$$

Answer

$$4x^2and\ 3x$$

Answer

$$4\ and\ (3x-2)$$

Question 2

Identify the factors of the given polynomial equation: y = 3x(x - 2)(x + 4).

Accepted Answer

3x, (x - 2), (x + 4)

Answer

3x, (x + 2), (x - 4)

Answer

3x, (x - 3), (x + 4)

Answer

3x, (x - 2), (x - 4)

Question 3

Identify the factors of the given polynomial equation: y = (x + 2)(x - 2).

Accepted Answer

(x + 2) and (x - 2)

Answer

(x + 2) and (x + 2)

Answer

(x - 2) and (x - 2)

Answer

(x + 1) and (x - 1)

Question 4

Identify the factors of the given polynomial equation: y = $$3x^2(4x^2 + 2)(x - 5)$$ .

Accepted Answer

$$3x^2$$ , $$4x^2 + 2$$ and $$x - 5$$

Answer

$$3x^2$$ , $$4x^2$$ , $$x - 5$$

Answer

$$3x^2$$ , $$2$$ , $$x - 5$$

Answer

$$3x^2$$ , $$4x^2 + 2$$ , 5

Question 5

Find the sum. $$\left( \frac{3}{4}x^2 - 2x + \frac{5}{6} \right) + \left( \frac{5}{4}x^2 + \frac{3}{2}x - \frac{1}{12} \right)$$ .

Accepted Answer

$$2x^2-\frac{1}{2}x+\frac{9}{12}$$

Answer

$$2x^2 + \frac{1}{2}x + \frac{9}{12}$$

Answer

$$\frac{8}{4}x^2+\frac{1}{2}x+\frac{9}{12}$$

Answer

$$\frac{8}{4}x^2-\frac{1}{2}x+\frac{9}{12}$$

Question 6

Find the sum. $$(2.3x^3 - 4.5x + 3) + (-7x^3 - 4.2x - 6)$$ .

Accepted Answer

$$-4.7x^3 - 8.7x - 3$$

Answer

$$-4.7x^3 - 8.7x - 9$$

Answer

$$-4.7x^3 - 0.3x - 3$$

Answer

$$-4.7x^3 - 0.3x - 9$$

Question 7

Find the sum. $$\left( \frac{5}{4}x^2 - \frac{3}{2}x - 2 \right) + \left( \frac{7}{8}x^2 - 5 \right)$$ .

Accepted Answer

$$\frac{17}{8}x^2-\frac{3}{2}x-7$$

Answer

$$\frac{17}{8}x^2-\frac{3}{2}x+7$$

Answer

$$\frac{17}{8}x^2-\frac{3}{2}x-5$$

Answer

$$\frac{17}{8}x^2-\frac{3}{2}x+5$$

Question 8

Find the sum. $$(-6.4x^2 + x - 3) + (-2x^2 - 3.2x + 1)$$ .

Accepted Answer

$$-8.4x^2 - 2.2x - 2$$

Answer

$$-8.4x^2 - 2.2x - 4$$

Answer

$$-4.4x^2 - 2.2x - 2$$

Answer

$$-8.4x^2 + 2.2x - 2$$

Question 9

Find the difference. $$(x^3-2.5x^2-3x-1.4)-(3x^2-4x-2)$$

Accepted Answer

$$x^3 - 5.5x^2 + x + 0.6$$

Answer

$$x^3 - 5.5x^2 + x - 0.6$$

Answer

$$x^3 - 5.5x^2 - x + 0.6$$

Answer

$$x^3 - 5.5x^2 - x - 0.6$$

Question 10

Find the difference. $$(\frac{1}{2} x^2 - 4x + 2.5)$$ - $$(\frac{3}{4} x^2 - 2.5x + 1)$$

Accepted Answer

$$-\frac{1}{4} x^2 - 1.5x + 1.5$$

Answer

$$\frac{1}{4}x^2-1.5x+1.5$$

Answer

$$-\frac{1}{4} x^2 + 1.5x + 1.5$$

Answer

$$\frac{1}{4}x^2-1.5x-1.5$$

Question 11

Find the difference. $$(3x^2+2x-\frac{5}{6})$$ - $$\left(\frac{6}{5}x^2+3.2x+\frac{11}{5}\right)$$

Accepted Answer

$$\frac{9}{5}x^2-1.2x-\frac{91}{30}$$

Answer

$$9x^2 - 1.2x - \frac{91}{5}$$

Answer

$$9x^2 - 1.2x - \frac{91}{6}$$

Answer

$$9x^2 - 1.2x - \frac{91}{10}$$

Question 12

Find the difference. $$\left(-4.25x^2+3x-2\right)-\left(1.75x^2-2.25x-1\right)$$

Accepted Answer

$$-6x^2 + 5.25x - 1$$

Answer

$$-6x^2 + 0.75x - 1$$

Answer

$$-6x^2 + 5.25x - 3$$

Answer

$$-6x^2 + 0.75x - 3$$

Question 13

Find the product: $$0.8x(1.2x^2-4x+1.8)$$

Accepted Answer

$$0.96x^3-3.2x^2+1.44x$$

Answer

$$0.96x^3-3.2x^2+1.44$$

Answer

$$0.96x^3-3.2x^2+1.44x+1.44$$

Answer

$$0.96x^3-3.2x^2+1.44x+0.8$$

Question 14

Find the product: $$-\frac{3}{4}x^3(3x^2y - \frac{1}{2}xy^2 - 4x + 3y)$$

Accepted Answer

$$-\frac{9}{4}x^5y + \frac{3}{8}x^4y^2 + 3x^4 - \frac{9}{4}x^3y$$

Answer

$$-\frac{9}{4}x^5y + \frac{3}{8}x^4y^2 + 3x^4 + \frac{9}{4}x^3y$$

Answer

$$-\frac{9}{4}x^5y - \frac{3}{8}x^4y^2 - 3x^4 + \frac{9}{4}x^3y$$

Answer

$$-\frac{9}{4}x^5y - \frac{3}{8}x^4y^2 - 3x^4 - \frac{9}{4}x^3y$$

Question 15

Find the product: $$0.5ab^3\left(4ab^5-\frac{3}{2}a^3b^2+\frac{5}{4}a^2b^5\right)$$

Accepted Answer

$$2a^2b^8-\frac{3}{4}a^4b^5+\frac{5}{8}a^3b^8$$

Answer

$$2ab^8-\frac{3}{4}a^3b^5+\frac{5}{8}a^2b^8$$

Answer

$$2a^2b^8+\frac{3}{4}a^4b^5+\frac{5}{8}a^3b^8$$

Answer

$$2a^2b^8-\frac{3}{4}a^4b^5-\frac{5}{8}a^3b^8$$

Question 16

Find the product: $$5x^2y^3\left(\frac{1}{10}x^3y^4-\frac{9}{8}xy^2+6x^4y\right)$$

Accepted Answer

$$\frac{1}{2}x^5y^7-\frac{45}{8}x^3y^5+30x^6y^4$$

Answer

$$\frac{1}{2}x^5y^7-\frac{45}{8}x^2y^5+30x^6y^3$$

Answer

$$\frac{1}{2}x^5y^7+\frac{45}{8}x^3y^5+30x^6y^5$$

Answer

$$\frac{1}{2}x^5y^7-\frac{45}{8}x^3y^5-30x^6y^6$$

Question 17

Find the product: $$\left(2x+3\right)\left(\frac{1}{5}x-\frac{8}{9}\right)$$

Accepted Answer

$$\frac{2}{5}x^2-\frac{53}{45}x-\frac{8}{3}$$

Answer

$$\frac{2}{5}x^2-\frac{53}{45}x-\frac{24}{9}$$

Answer

$$\frac{2}{5}x^2-\frac{16}{15}x-\frac{8}{3}$$

Answer

$$\frac{2}{5}x^2 - \frac{16}{15}x - \frac{24}{9}$$

Question 18

Find the product: $$\left(1.2x+3.5\right)\left(4x-\frac{6}{5}\right)$$

Accepted Answer

$$4.8x^2+12.56x-4.2$$

Answer

$$4.8x^2+12.56x-0.72$$

Answer

$$4.8x^2 + 14x - 4.2$$

Answer

$$4.8x^2 + 14x - 0.72$$

Question 19

Find the product: $$\left(\frac{1}{2}x+3\right)\left(\frac{2}{3}x^2-5x+9\right)$$

Accepted Answer

$$\frac{1}{3}x^3-\frac{1}{2}x^2-10.5x+27$$

Answer

$$\frac{1}{3}x^2-\frac{1}{2}x-10.5+27$$

Answer

$$\frac{1}{3}x^3 - \frac{5}{2}x^2 + \frac{29}{2}x + 15$$

Answer

$$\frac{1}{3}x^3 - \frac{5}{2}x^2 + \frac{29}{2}x - 27$$

Question 20

Find the product: $$(\frac{1}{3}x + 2)(\frac{1}{3}x - 2)$$

Accepted Answer

$$\frac{1}{9}x^2 - 4$$

Answer

$$\frac{1}{9}x^2 + 4$$

Answer

$$\frac{1}{3}x^2 - 4$$

Answer

$$\frac{1}{3}x^2 + 4$$

Question 21

Find the Quotient: $$\frac{3x^2-4x-1.2}{\frac{2}{3}x}$$ .

Accepted Answer

$$\frac{9}{2}x-6-\frac{1.8}{x}$$

Answer

$$\frac{9}{2}x-6-1.8x^{-1}$$

Answer

$$\frac{9}{2}x-6-1.8x$$

Answer

$$\frac{\frac{9}{2}x-6}{-1.8x}$$

Question 22

Find the Quotient: $$\frac{9b^4 - 27b^3 - b - 2}{3b}$$ .

Accepted Answer

$$3b^3-9b^2-\frac{1}{3}-\frac{2}{3b}$$

Answer

$$3b^3-9b^2-\frac{1}{3}-\frac{2}{3}b^{-1}$$

Answer

$$\frac{3b^3-9b^2-\frac{1}{3}}{-6b}$$

Answer

$$\frac{3b^3-9b^2-\frac{5}{3}}{3b}$$

Question 23

Find the Quotient: $$(x^2y^5 - 4xy^3 + 10xy) \div (6xy)$$ .

Accepted Answer

$$\frac{1}{6}xy^4-\frac{2}{3}y^2+\frac{5}{3}$$

Answer

$$\frac{1}{6}x^2y^5-\frac{2}{3}xy^3+\frac{5}{3}xy$$

Answer

$$\frac{1}{6}xy^4+\frac{2}{3}y^2-\frac{5}{3}$$

Answer

$$6xy^4-\frac{2}{3}y^2+\frac{5}{3}$$

Question 24

Rewrite each polynomial expression as a product of polynomials. $$12a^4b^3 - 15a^3b^2 + 9a^2b^4 - 6ab$$

Accepted Answer

$$3ab(4a^3b^2 - 5a^2b + 3ab^3 - 2)$$

Answer

$$6ab(2a^3b^2 - 2.5a^2b + 1.5ab^3 - 1)$$

Answer

$$3ab(4a^4b^3-5a^3b^2+3a^2b^4-2ab)$$

Answer

$$3ab(4a^4b^3-5a^3b^2+3a^2b^4-2)$$

Question 25

Rewrite each polynomial expression as a product of polynomials. $$16x^2 + 24x + 9$$

Select all the possible answers.

Accepted Answer

$$(4x + 3)^2$$

Accepted Answer

$$\left(4x+3\right)\left(4x+3\right)$$

Answer

(4x + 1)(4x + 9)

Answer

(8x + 3)(2x + 3)

Question 26

Rewrite each polynomial expression as a product of polynomials. $$2x^3 + 4x^2 + 2x + 4$$

Select all possible answers.

Accepted Answer

$$2(x^3 + 2x^2 + x + 2)$$

Accepted Answer

$$2(x^2+1)(x+2)$$

Accepted Answer

$$\left(2x^2+2\right)\left(x+2\right)$$

Answer

$$2(x^2 + 2x + 1)(x + 2)$$

Answer

$$2(x + 1)(x^2 + 2)$$

Question 27

Rewrite the polynomial expression $$x^2 + 11x + 24$$ as a product of polynomials.

Accepted Answer

(x + 3)(x + 8)

Answer

(x + 4)(x + 6)

Answer

(x + 2)(x + 12)

Answer

(x + 1)(x + 24)

Question 28

Rewrite the polynomial expression $$3x^2 - 8x + 4$$ as a product of polynomials.

Accepted Answer

(3x - 2)(x - 2)

Answer

(3x + 2)(x + 2)

Answer

(3x - 4)(x - 1)

Answer

(3x + 4)(x - 1)

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