$$3.6 \times 10^9$ and 3$$,600,000,000$$

Question 1

Given the polynomial $$8x^3$$ - $$9x^8$$ + $$3x^2$$, what is its degree and what type of polynomial is it?

Accepted Answer

Degree: 8, Type: Trinomial

Question 2

Simplify the following expression and select the correct answer: $$(3x^2 - 7x + 8) + (4x^2 + 5x - 10)$$

Accepted Answer

$$7x^2 - 2x - 2$

Question 3

Subtract the following polynomials: $$(5x^2 - 4x + 3) - (x^2 + 8x - 12)$$

Accepted Answer

$$4x^2 - 12x + 15$

Question 4

Write $$5,876,000,000 in $$scientific notation.

Accepted Answer

$$5.876 	imes 10^9$

Question 5

Express $$0.000000000068 in $$scientific notation.

Accepted Answer

$$6.8 	imes 10$$^{-11}$$

Question 6

Convert $$2.98 	imes 10$$^{-6}$$ to standard notation.

Accepted Answer

$$0.00000298$$

Question 7

Convert $$7.39 	imes 10$$^{12}$$ to standard notation.

Accepted Answer

$$7,390,000,000,000$$

Question 8

Multiply and write your answer in both scientific and standard notation: $$(4 	imes 10^3)(9 	imes 10^5)$$

Accepted Answer

$$3.6 	imes 10^9$ and 3$$,600,000,000$$

Question 9

Simplify and write your answer in scientific notation: $$(2.6 	imes 10^{-4})^2 	imes 10^2$$

Accepted Answer

$$6.76 	imes 10$$^{-6}$$

Question 10

Simplify $$(2x)^3$$ and write your answer with only positive exponents.

Accepted Answer

$$8x^3$$

Question 11

Multiply: $$3x^3(4x^2$ + 7x - 5)$

Accepted Answer

$$12x^5$$ + $$21x^4$$ - $$15x^3$$

Question 12

Multiply: $$(2x + 7y)(3x - 4y)$$

Accepted Answer

$$6x^2 - 8xy + 21xy$$ - $$28y^2$$ = $$6x^2 + 13xy$$ - $$28y^2$$

Question 13

Multiply: $$(x + 6)(x - 6)$$

Accepted Answer

$$x^2 - 36$

Question 14

Expand and simplify: $$(2x + 6)^2$

Accepted Answer

$$4x^2 + 12x + 36$

Question 15

Multiply: $$3x^3(x + 3)(2x - 5$$)$$

Accepted Answer

$$6x^5$$ + $$9x^4$$ - $$15x^4$$ - $$45x^3$$ = $$6x^5$$ - $$6x^4$$ - $$45x^3$$

Question 16

Multiply: $$(3x + 1)(4x^2$ + 2x + 3)$$

Accepted Answer

$$12x^3$$ + $$10x^2 + 11x + 3$

Question 17

Multiply: $$(2x^2 - 3x$$ + $$2)(3x^2 + 5x - 6$$)$$

Accepted Answer

$$6x^4$$ + $$x^3$$ - $$22x^2 + 31x - 12$

Question 18

Expand: $$(x + 3)^3$

Accepted Answer

$$x^3$$ + $$9x^2 + 27x + 27$

Question 19

A scientist needs to dilute a solution from $$5.0 	imes 10$$^{-3}$$ M to 2.5$$ 	imes $$10^{-4} M. By $$what factor should the solution be diluted?

Accepted Answer

$$20$$

Polynomial Operations, Scientific Notation, and Exponents – Guided Practice

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