Sr. Mary Rebekah 1 - Survivor Math · When multiplying two powers with the same base, add the exponents. Example: Simplify 3 6 5 2. For any number a and all integers m and n, (am)n

Sr. Mary Rebekah 1

NAME:

Today we will: Define monomials. Multiply monomials. Simplify expressions involving monomials.

Sr. Mary Rebekah 2

What is a monomial?

What is a Constant?

Examples of Monomials

For any number a and all integers m and n, am

∙ an = am+n When multiplying two powers with the same base, add the

exponents.

Example:

Simplify 3𝑥6 5𝑥2 .

For any number a and all integers m and n, (am

)n = amn

When taking the power of another power, multiply the

exponents.

Example:

Simplify (−2𝑎𝑏2)3.

Example:

Simplify 3𝑥 2.

For any number a and all integers m and n, (ab)m= am

∙ bm When finding the power of a

product, find the power of each factor and multiply.

1. 2𝑥2𝑦3𝑧4 3 𝑥2𝑧 4

2. −3 2𝑥 4 4𝑥5𝑦 2

NAME:

Today we will: Find the QUOTIENT of two monomials. Simplify expressions containing negative and zero exponents.

Sr. Mary Rebekah 3

Quotients of Monomials

Sr. Mary Rebekah 3

For any a ≠ 0 and any integers m and p, 𝑎𝑚

𝑎𝑝 = am-p When dividing two powers with the same base, subtract the

exponents.

Example:

Simplify 𝑥3𝑦4

𝑥2𝑦.

For any number a and b ≠ 0, and any integer m, 𝑎

𝑏

𝑚=

𝑎𝑚

𝑏𝑚

. When taking the power of another exponent, multiply the exponents

together and keep the base.

Example:

Simplify5𝑥2𝑦

6

2

.

Example:

Simplify 35

35.

A zero exponent is a non-zero number raised to the zero power. For any a ≠ 0, a

0

= 1. A power of zero is one.

We can use the principles for reducing fraction to find the

quotients of monomials like …

27 2 ∙2 ∙2 ∙2 ∙2 ∙2 ∙2

24 2 ∙2 ∙2 ∙2 =

=

A non-zero number raised to a negative power is a negative exponent. For any a ≠ 0 and any integer n, a

-n = 1 /an.

Investigate:

Example: 𝑛−5𝑝4

𝑟−2

-63= (-6)2=

so many digits

Sometimes with numbers this small or this large, it

can be helpful to rewrite without the extra zeroes.

SCIENTIFIC NOTATION

becomes becomes

The rewritten format is called

Moving the decimal point to

the LEFT

represents…

Moving the decimal point to

the RIGHT

represents….

Name:

When converting a number into scientific notation,

If you moved a decimal

to the

LEFT power of ten

When writing scientific notation,

If you moved a decimal to the

power of ten

G

Write 0.0337 in scientific notation

RI HT NE ATIVE

POSI IVE

So, we ____ the 1st non-zero digit, place a _____ ____

before the next, and use powers of _____ to correctly

represent how we moved the decimal point.

SCIENTIFIC NOTATION PRACTICE

8 x 100 = 5 100 = 0.6 X 1000 = 0.9 1000=

Powers of Ten

Dividing by 100 is the same as multiplying by ten to the what power? ____

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When we UN-DO an

operation, we do the

OPPOSITE (Inverse

operations)!

NAME:

Today we will: Define polynomial. Determine the degree of a polynomial. Write polynomials in standard from.

Sr. Mary Rebekah 6

What is a polynomial?

How do I determine the degree of a polynomial?

Expression Is it a

polynomial? Monomial, binomial,

or trinomial?

4𝑦 − 5𝑥𝑧

−6.5

7𝑎−3 + 9𝑏

5𝑥2 + 7𝑥 − 2𝑥 + 9

1

2

3

4

5

NAME:

Today we will: Add polynomials. Subtract polynomials.

Sr. Mary Rebekah 7

1 (6x3-4)+(-2x3+9)

2 (x3-x2+5x+6)-(x2+2x)

3 (-4x3-2x+8)-(4x3+3x2-5)

-3y2+3y-12

9x-6

-xy2+6xy-10

9x+4y-17z

4 (8y-4y3)+(3y-9y3)

Cut an paste each expression into your interactive notebook. Simplify each them, showing your work underneath the paper strip. Then cut each piece from the right side

of the page and match the answers to the expressions below.

5 (4y2+2y-8)-(7y2+4-y)

6 (x3-3x+1)-(x3+7-12x)

(xy2+2xy-4)+(-6+4xy-2xy2)

(4x+2y-6z)+(5y-2z+7x)-(9z+2x+3y)

-13y2+11y

-8x3-3x2-2x+13

4x3+5

x3-2x2+3x+6

NAME:

Today we will: Multiply a polynomial by a monomial. Solve equations involving the products of monomials and polynomials.

Sr. Mary Rebekah 8

1

2

3

Find -3x2(7x2-x+4).

Find -6d3(3d4-2d2-d+9).

Simplify 5a2(-4a2+2a-7)-2a (a2+a-3).

4

5

6

Solve for x. -6(11-2c)=7(-2-2c) 2x(x+4)+7 = (x+8) +2x(x+1)+12 Marlene is buying a new plasma television. The height of the screen of the television is one half the width plus 5 inches. The width is 30 inches. Find the height of the screen in inches.

NAME:

Today we will: Multiply binomials using the FOIL method. Multiply polynomials by using the Distributive Property.

Sr. Mary Rebekah 9

F O I L

Find each product. (6x+5)(2x2-3x-5) (2x2+3x-1)(3x2-5x+2)

irst uter nner ast

(2x-7)(3x+5)

1 2

1. (x+5)(x+2) 2. (2a+9)(5a-6) 3. (y-2)(2y2-y+4) 4. Find an expression to represent the area of the shaded region of the

figure shown.

4x+1

5x 2x-3

+

-

+ -

Sr. Mary Rebekah 11

Give an example of each of the following vocab words (or use the ones on pg. 459): Binomial Constant Degree of a monomial Degree of a polynomial FOIL Method Leading coefficient Monomial Order of magnitude Polynomial Quadratic expression Scientific notation Standard form of a polynomial Trinomial