Polynomials and Materials in Algebra

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Questions and Answers

What is the quotient of the monomial $-15x^2$ divided by $-3x$?

$-5x$

$-5x^2$

$5x$ (correct)

$15x$

The division statement represented by the algebra tiles shows a positive quotient.

False

What is the division statement represented by the algebra tiles with $-12x^2$ and $2x$?

$-6x$

The quotient of $10xy$ divided by $2x$ is _____

5y Signup and view all the answers

Match the following algebra expressions with their corresponding division statements:

$-12x^2 ÷ 3x$ = $-4x$ $8x ÷ 2x$ = $4$ $-9x^2 ÷ -3x$ = $3x$ $15xy ÷ 5y$ = $3x$ Signup and view all the answers

What is the product of the monomials (2x)(4x)?

8x^2 Signup and view all the answers

The product of (-4x) and (2x) is positive.

False Signup and view all the answers

What is the area of a rectangle with a width of 3.9x and a length of 5x?

19.5x^2 Signup and view all the answers

The product of (-3r) and (-2t) is _____ .

6rt Signup and view all the answers

Match the multiplication statements with their corresponding products:

(3n)(2n) = 6n^2 (-4k)(-7k) = 28k^2 (-4w)(2.5w) = -10w^2 (8m)(-0.5n) = -4mn Signup and view all the answers

Which multiplication statement results in a product of negative value?

(-4x)(2x) Signup and view all the answers

The expression for the area of a parallelogram with a base of 8.1z and a height of 4.2z is 34.02z^2.

True Signup and view all the answers

What is the product of (3a)(-6b)?

-18ab Signup and view all the answers

What is the equivalent expression for $-2x - 4x$?

$-6x$ Signup and view all the answers

The product of $3y$ and $2.7y$ is $6.3y^2$.

True Signup and view all the answers

What is the product of $12h$ and $h + 2$?

$12h^2 + 24h$ Signup and view all the answers

The expression $15y - 10y$ simplifies to __________.

$5y$ Signup and view all the answers

What is a polynomial multiplication expression equivalent to $24d^2 - 12d$?

$6d(4d - 2)$ Signup and view all the answers

Match the following expressions to their simplified forms:

$4x$ = $-4$ $-6x^2$ = $24d^2 - 12d$ $-3y + 2$ = $-3y - 2$ $-2x$ = $2x$ Signup and view all the answers

The expression $(2.4x)(4y)$ calculates to __________.

$9.6xy$ Signup and view all the answers

Show the steps for calculating $-6x^2 imes -3x$.

Multiply coefficients: $6*3 = 18$; Combine $x^2$ and $x$ to get $18x^3$. Signup and view all the answers

What is the expression for the area of a rectangle with length $2xy$ and area $12x^2y + 6xy^2$?

Width = $3y$ Signup and view all the answers

A shape's area can never be negative.

True Signup and view all the answers

If the radius of a circle is $r$, what is the formula for the area of the circle?

$\pi r^2$ Signup and view all the answers

When finding the perimeter of a rectangle with length $l$ and width $w$, the formula is $2(l + ______)$.

w Signup and view all the answers

Match the expressions with their correct meanings:

$3.6gf + 0.93g$ = Combining like terms $2x - 3$ = Linear expression $18$ = Area of rectangle $5cm$ = Depth of gravel Signup and view all the answers

What is the range of area for each parking lot design?

200 m² to 650 m² Signup and view all the answers

A depth of 5 cm is equivalent to 0.05 m.

True Signup and view all the answers

What is the ratio of the area of a square inscribed in a circle to the area of the circle if the circle has a radius $r$?

$\frac{1}{2}$ Signup and view all the answers

What is the result of dividing $-4.8x^2$ by $1.2x$?

-4x Signup and view all the answers

The expression $3yz$ can be simplified to $3y + z$.

False Signup and view all the answers

What is the polynomial formed by multiplying $(3yz)$ and $(4)$?

12yz Signup and view all the answers

The result of $2xy ÷ 2x$ is _____

y Signup and view all the answers

What is the resulting factor when simplifying $2x(3x - 5)$?

6x^2 - 10 Signup and view all the answers

The polynomial $5x(3 - 2y)$ can be expanded to $15x - 10xy$.

True Signup and view all the answers

Match the following polynomial expressions with their simplified form:

$-3x + 2$ = $2 - 3x$ $15x - 10xy$ = $5x(3 - 2y)$ $9x ÷ 3x$ = $3$ $6x^2 - 10x$ = $2x(3x - 5)$ Signup and view all the answers

The expression $(-3x)(-8x)$ simplifies to _____

24x^2 Signup and view all the answers

What is an example of a polynomial expression?

5x + 3 Signup and view all the answers

All polynomial expressions can only include whole number exponents.

True Signup and view all the answers

What is the expression for the area of a backyard if its length is represented by 'l' and width by 'w'?

l * w Signup and view all the answers

The expression $8c + 3 - 5c + 1$ simplifies to ____.

3c + 4 Signup and view all the answers

Match the following expressions with their corresponding simplified forms:

8c + 3 - 5c + 1 = 3c + 4 -1 + x - 1 - x + 1 = 0 2x + 2x^2 = 2x + 2x^2 9 - 3 = 6 Signup and view all the answers

If the park is divided into three equal sections, what would be the side length of each section if the side measurement is represented as $2n + 4$?

2n + 4 Signup and view all the answers

The perimeter of a rectangular backyard can be calculated using the expression $2(l + w)$.

True Signup and view all the answers

What is the result of selling 15 comics, 7 hardcover books, and 5 paperbacks if comics, hardcover books, and paperbacks have a price of $3, $15, and $10 respectively?

$100 Signup and view all the answers

Study Notes

Polynomials

Polynomials have been used for centuries to describe relationships
They're useful in everyday life, such as calculating costs in landscaping projects
Polynomials save time by offering various possible costs
Polynomials may be helpful in other professions.

Key Words

Monomial
Polynomial
Binomial
Distributive property

Materials and Folding

A sheet of 11 x 17 paper is used to make a foldable
Two sheets of 8.5 x 11 paper are used
Scissors, staples, rulers, grid paper are also needed.

Steps

The 11 x 17 sheet needs to be folded in half
The outer edges need to be folded to meet in the middle
Label the fold according to directions
The shorter side (8.5 x 11) sheets are also folded in half, opposite directions
Two-tab books will be formed
Label these tabbed books for clarity

Studying That Suits You

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Description

Explore the concept of polynomials in this quiz, where you will learn about their significance in various fields and practical applications. Additionally, discover how to create an organized foldable project using simple materials and methods. Test your knowledge on both theoretical and practical aspects!

Polynomials and Materials in Algebra

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Podcast

Questions and Answers

What is the quotient of the monomial $-15x^2$ divided by $-3x$?

The division statement represented by the algebra tiles shows a positive quotient.

What is the division statement represented by the algebra tiles with $-12x^2$ and $2x$?

The quotient of $10xy$ divided by $2x$ is _____

Match the following algebra expressions with their corresponding division statements:

What is the product of the monomials (2x)(4x)?

The product of (-4x) and (2x) is positive.

What is the area of a rectangle with a width of 3.9x and a length of 5x?

The product of (-3r) and (-2t) is _____ .

Match the multiplication statements with their corresponding products:

Which multiplication statement results in a product of negative value?

The expression for the area of a parallelogram with a base of 8.1z and a height of 4.2z is 34.02z^2.

What is the product of (3a)(-6b)?

What is the equivalent expression for $-2x - 4x$?

The product of $3y$ and $2.7y$ is $6.3y^2$.

What is the product of $12h$ and $h + 2$?

The expression $15y - 10y$ simplifies to __________.

What is a polynomial multiplication expression equivalent to $24d^2 - 12d$?

Match the following expressions to their simplified forms:

The expression $(2.4x)(4y)$ calculates to __________.

Show the steps for calculating $-6x^2 imes -3x$.

What is the expression for the area of a rectangle with length $2xy$ and area $12x^2y + 6xy^2$?

A shape's area can never be negative.

If the radius of a circle is $r$, what is the formula for the area of the circle?

When finding the perimeter of a rectangle with length $l$ and width $w$, the formula is $2(l + ______)$.

Match the expressions with their correct meanings:

What is the range of area for each parking lot design?

A depth of 5 cm is equivalent to 0.05 m.

What is the ratio of the area of a square inscribed in a circle to the area of the circle if the circle has a radius $r$?

What is the result of dividing $-4.8x^2$ by $1.2x$?

The expression $3yz$ can be simplified to $3y + z$.

What is the polynomial formed by multiplying $(3yz)$ and $(4)$?

The result of $2xy ÷ 2x$ is _____

What is the resulting factor when simplifying $2x(3x - 5)$?

The polynomial $5x(3 - 2y)$ can be expanded to $15x - 10xy$.

Match the following polynomial expressions with their simplified form:

The expression $(-3x)(-8x)$ simplifies to _____

What is an example of a polynomial expression?

All polynomial expressions can only include whole number exponents.

What is the expression for the area of a backyard if its length is represented by 'l' and width by 'w'?

The expression $8c + 3 - 5c + 1$ simplifies to ____.

Match the following expressions with their corresponding simplified forms:

If the park is divided into three equal sections, what would be the side length of each section if the side measurement is represented as $2n + 4$?

The perimeter of a rectangular backyard can be calculated using the expression $2(l + w)$.

What is the result of selling 15 comics, 7 hardcover books, and 5 paperbacks if comics, hardcover books, and paperbacks have a price of $3, $15, and $10 respectively?

Study Notes

Polynomials

Key Words

Materials and Folding

Steps

Studying That Suits You

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