Question
Six statements about polynomials are given. Select all the statements that are true(3 points)
Responses
5x2y − 6xy3z + 3x5
is a fifth degree polynomial
5x2y − 6xy3z + 3x5
is a fifth degree polynomial
5x2y − 6xy3z + 3x5
contains four terms
5x2y − 6xy3z + 3x5
contains four terms
5x2y − 6xy3 + 3x5
has a leading coefficient of 3
5x2y − 6xy3 + 3x5
has a leading coefficient of 3
12a5 − 7 +3a7+11a
is equivalent to 3a7 + 12a5 + 11a − 7
12a5 − 7 +3a7+11a
is equivalent to 3a7 + 12a5 + 11a − 7
12a5 − 7 +3a7+11a
has a leading term of 12a5
12a5 − 7 +3a7+11a
has a leading term of 12 A to the 5th power
12a5 − 7 +3a7+11a
has a contant of 7
Responses
5x2y − 6xy3z + 3x5
is a fifth degree polynomial
5x2y − 6xy3z + 3x5
is a fifth degree polynomial
5x2y − 6xy3z + 3x5
contains four terms
5x2y − 6xy3z + 3x5
contains four terms
5x2y − 6xy3 + 3x5
has a leading coefficient of 3
5x2y − 6xy3 + 3x5
has a leading coefficient of 3
12a5 − 7 +3a7+11a
is equivalent to 3a7 + 12a5 + 11a − 7
12a5 − 7 +3a7+11a
is equivalent to 3a7 + 12a5 + 11a − 7
12a5 − 7 +3a7+11a
has a leading term of 12a5
12a5 − 7 +3a7+11a
has a leading term of 12 A to the 5th power
12a5 − 7 +3a7+11a
has a contant of 7
Answers
Answered by
Scar
Use the distributive property to find the product of x(3x +5x2−7−6x)
. Write your answer in standard form.(1 point)
Responses
5x3−3x2+7x
5 x cubed minus 3 x squared plus 7 x
5x2−3x−7
5 x squared minus 3 x minus 7
−7x + 5x3−3x2
−7x + 5x3−3x2
5x3−3x2−7x
5 x cubed minus 3 x squared minus 7 x
3x2+5x3−7x − 6x2
3x2+5x3−7x − 6x2
5x3+3x2+7x
5 x cubed plus 3 x squared plus 7 x
5x3−9x2+7x
5 x cubed minus 9 x squared plus 7 x
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page 10 of 10
. Write your answer in standard form.(1 point)
Responses
5x3−3x2+7x
5 x cubed minus 3 x squared plus 7 x
5x2−3x−7
5 x squared minus 3 x minus 7
−7x + 5x3−3x2
−7x + 5x3−3x2
5x3−3x2−7x
5 x cubed minus 3 x squared minus 7 x
3x2+5x3−7x − 6x2
3x2+5x3−7x − 6x2
5x3+3x2+7x
5 x cubed plus 3 x squared plus 7 x
5x3−9x2+7x
5 x cubed minus 9 x squared plus 7 x
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page 10 of 10
Answered by
Scar
If M = 10xy +3y−4
and N = 9y+5xy+14
, then what is M−N
?(1 point)
Responses
5xy−6y−18
5 x y minus 6 y minus 18
−5xy−6y−18
negative 5 x y minus 6 y minus 18
5xy+8y+18
5 x y plus 8 y plus 18
5xy+6y−14
5 x y plus 6 y minus 14
15xy+6y+14
15 x y plus 6 y plus 14
and N = 9y+5xy+14
, then what is M−N
?(1 point)
Responses
5xy−6y−18
5 x y minus 6 y minus 18
−5xy−6y−18
negative 5 x y minus 6 y minus 18
5xy+8y+18
5 x y plus 8 y plus 18
5xy+6y−14
5 x y plus 6 y minus 14
15xy+6y+14
15 x y plus 6 y plus 14
Answered by
Scar
m=10xy+3y-4
n=9y+5xy+14
m-n?
n=9y+5xy+14
m-n?
Answered by
GPT-4o mini
Let's evaluate the given statements about the polynomials:
1. **5x²y - 6xy³z + 3x⁵ is a fifth degree polynomial**
- **True:** The highest degree term is 3x⁵, which has a degree of 5.
2. **5x²y - 6xy³z + 3x⁵ contains four terms**
- **False:** There are three terms in this polynomial: 5x²y, -6xy³z, and 3x⁵.
3. **5x²y - 6xy³ + 3x⁵ has a leading coefficient of 3**
- **True:** The leading term is 3x⁵, and its leading coefficient is 3.
4. **12a⁵ - 7 + 3a⁷ + 11a is equivalent to 3a⁷ + 12a⁵ + 11a - 7**
- **True:** The terms can be rearranged in any order since addition is commutative.
5. **12a⁵ - 7 + 3a⁷ + 11a has a leading term of 12a⁵**
- **False:** The leading term is 3a⁷ because it has the highest degree.
6. **12a⁵ - 7 + 3a⁷ + 11a has a constant of 7**
- **False:** The constant term is -7 (the -7 in the polynomial).
Based on this analysis, the **true statements** are:
- 5x²y - 6xy³z + 3x⁵ is a fifth degree polynomial.
- 5x²y - 6xy³ + 3x⁵ has a leading coefficient of 3.
- 12a⁵ - 7 + 3a⁷ + 11a is equivalent to 3a⁷ + 12a⁵ + 11a - 7.
1. **5x²y - 6xy³z + 3x⁵ is a fifth degree polynomial**
- **True:** The highest degree term is 3x⁵, which has a degree of 5.
2. **5x²y - 6xy³z + 3x⁵ contains four terms**
- **False:** There are three terms in this polynomial: 5x²y, -6xy³z, and 3x⁵.
3. **5x²y - 6xy³ + 3x⁵ has a leading coefficient of 3**
- **True:** The leading term is 3x⁵, and its leading coefficient is 3.
4. **12a⁵ - 7 + 3a⁷ + 11a is equivalent to 3a⁷ + 12a⁵ + 11a - 7**
- **True:** The terms can be rearranged in any order since addition is commutative.
5. **12a⁵ - 7 + 3a⁷ + 11a has a leading term of 12a⁵**
- **False:** The leading term is 3a⁷ because it has the highest degree.
6. **12a⁵ - 7 + 3a⁷ + 11a has a constant of 7**
- **False:** The constant term is -7 (the -7 in the polynomial).
Based on this analysis, the **true statements** are:
- 5x²y - 6xy³z + 3x⁵ is a fifth degree polynomial.
- 5x²y - 6xy³ + 3x⁵ has a leading coefficient of 3.
- 12a⁵ - 7 + 3a⁷ + 11a is equivalent to 3a⁷ + 12a⁵ + 11a - 7.
Answered by
GPT-4o mini
To find the product of \( x(3x + 5x^2 - 7 - 6x) \) using the distributive property, we will distribute \( x \) to each term inside the parentheses.
### Step-by-step:
1. Distribute \( x \) to each term:
- \( x \cdot 3x = 3x^2 \)
- \( x \cdot 5x^2 = 5x^3 \)
- \( x \cdot (-7) = -7x \)
- \( x \cdot (-6x) = -6x^2 \)
So, after distributing, we have:
\[ 3x^2 + 5x^3 - 7x - 6x^2 \]
2. Now, combine like terms:
- Combine \( 3x^2 \) and \( -6x^2 \):
\[ 3x^2 - 6x^2 = -3x^2 \]
- The \( 5x^3 \) remains as is.
- The \( -7x \) remains as is.
Thus, we now have:
\[ 5x^3 - 3x^2 - 7x \]
### Final Answer in Standard Form:
The final expression written in standard form is:
\[ 5x^3 - 3x^2 - 7x \]
From the options provided, the correct choice is:
**5x³ - 3x² - 7x**
### Step-by-step:
1. Distribute \( x \) to each term:
- \( x \cdot 3x = 3x^2 \)
- \( x \cdot 5x^2 = 5x^3 \)
- \( x \cdot (-7) = -7x \)
- \( x \cdot (-6x) = -6x^2 \)
So, after distributing, we have:
\[ 3x^2 + 5x^3 - 7x - 6x^2 \]
2. Now, combine like terms:
- Combine \( 3x^2 \) and \( -6x^2 \):
\[ 3x^2 - 6x^2 = -3x^2 \]
- The \( 5x^3 \) remains as is.
- The \( -7x \) remains as is.
Thus, we now have:
\[ 5x^3 - 3x^2 - 7x \]
### Final Answer in Standard Form:
The final expression written in standard form is:
\[ 5x^3 - 3x^2 - 7x \]
From the options provided, the correct choice is:
**5x³ - 3x² - 7x**
Answered by
GPT-4o mini
To find \( M - N \) where \( M = 10xy + 3y - 4 \) and \( N = 9y + 5xy + 14 \), we will perform the subtraction step by step.
### Step 1: Write the expression for \( M - N \)
\[
M - N = (10xy + 3y - 4) - (9y + 5xy + 14)
\]
### Step 2: Distribute the negative sign
\[
M - N = 10xy + 3y - 4 - 9y - 5xy - 14
\]
### Step 3: Combine like terms
1. **Combine the \( xy \) terms:**
\[
10xy - 5xy = 5xy
\]
2. **Combine the \( y \) terms:**
\[
3y - 9y = -6y
\]
3. **Combine the constant terms:**
\[
-4 - 14 = -18
\]
### Step 4: Write the final expression
Combining all the results gives:
\[
M - N = 5xy - 6y - 18
\]
### Final Answer
So, the answer for \( M - N \) is:
**5xy - 6y - 18**
### Step 1: Write the expression for \( M - N \)
\[
M - N = (10xy + 3y - 4) - (9y + 5xy + 14)
\]
### Step 2: Distribute the negative sign
\[
M - N = 10xy + 3y - 4 - 9y - 5xy - 14
\]
### Step 3: Combine like terms
1. **Combine the \( xy \) terms:**
\[
10xy - 5xy = 5xy
\]
2. **Combine the \( y \) terms:**
\[
3y - 9y = -6y
\]
3. **Combine the constant terms:**
\[
-4 - 14 = -18
\]
### Step 4: Write the final expression
Combining all the results gives:
\[
M - N = 5xy - 6y - 18
\]
### Final Answer
So, the answer for \( M - N \) is:
**5xy - 6y - 18**
Answered by
GPT-4o mini
To find \( m - n \) where
\[
m = 10xy + 3y - 4
\]
and
\[
n = 9y + 5xy + 14,
\]
we will perform the subtraction step by step.
### Step 1: Write the expression for \( m - n \)
\[
m - n = (10xy + 3y - 4) - (9y + 5xy + 14)
\]
### Step 2: Distribute the negative sign
Distributing the negative sign to the terms in \( n \):
\[
m - n = 10xy + 3y - 4 - 9y - 5xy - 14
\]
### Step 3: Combine like terms
1. **Combine the \( xy \) terms:**
\[
10xy - 5xy = 5xy
\]
2. **Combine the \( y \) terms:**
\[
3y - 9y = -6y
\]
3. **Combine the constant terms:**
\[
-4 - 14 = -18
\]
### Step 4: Write the final expression
Combining all the results gives:
\[
m - n = 5xy - 6y - 18
\]
### Final Answer
So, the result for \( m - n \) is:
\[
\boxed{5xy - 6y - 18}
\]
\[
m = 10xy + 3y - 4
\]
and
\[
n = 9y + 5xy + 14,
\]
we will perform the subtraction step by step.
### Step 1: Write the expression for \( m - n \)
\[
m - n = (10xy + 3y - 4) - (9y + 5xy + 14)
\]
### Step 2: Distribute the negative sign
Distributing the negative sign to the terms in \( n \):
\[
m - n = 10xy + 3y - 4 - 9y - 5xy - 14
\]
### Step 3: Combine like terms
1. **Combine the \( xy \) terms:**
\[
10xy - 5xy = 5xy
\]
2. **Combine the \( y \) terms:**
\[
3y - 9y = -6y
\]
3. **Combine the constant terms:**
\[
-4 - 14 = -18
\]
### Step 4: Write the final expression
Combining all the results gives:
\[
m - n = 5xy - 6y - 18
\]
### Final Answer
So, the result for \( m - n \) is:
\[
\boxed{5xy - 6y - 18}
\]