Asked by Yes.
The result of adding 2 polynomials results in another polynomial, meaning that polynomials are closed under addition.(1 point)
Responses
True
False
Responses
True
False
Answers
Answered by
Yes.
Johnny wonders if he can relate the sum and difference of two polynomials, using the equations shown.
-(K + F) = K - F.
Are the two expressions shown equivalent to each other? What evidence supports or disproves the statement? Pick the statement below that clearly explains your answer, remembering to justify by listing the property used.
Responses:
YES - the two expressions are equivalent because -(K + F) = K - F and I used the negative property of multiplication to solve.
NO - they are not equivalent because -(K + F) = -K + -F. I used the Distributive Property to simplify the left side.
YES - they are equivalent because -(K + F) = -K + F and then you can switch the - to the F. I used the Commutative Property to change the signs of the K and the F.
NO - they are not equivalent because -(K + F) = -K + F and that is not the correct way it is written above. I used the Distributive Property.
-(K + F) = K - F.
Are the two expressions shown equivalent to each other? What evidence supports or disproves the statement? Pick the statement below that clearly explains your answer, remembering to justify by listing the property used.
Responses:
YES - the two expressions are equivalent because -(K + F) = K - F and I used the negative property of multiplication to solve.
NO - they are not equivalent because -(K + F) = -K + -F. I used the Distributive Property to simplify the left side.
YES - they are equivalent because -(K + F) = -K + F and then you can switch the - to the F. I used the Commutative Property to change the signs of the K and the F.
NO - they are not equivalent because -(K + F) = -K + F and that is not the correct way it is written above. I used the Distributive Property.
Answered by
Yes.
Find the product: W×G
W=3x−2 and G=4x−1
Responses
12x2−5x−2
12x2−11x+2
7x2−9x−2
x2−10x+2
W=3x−2 and G=4x−1
Responses
12x2−5x−2
12x2−11x+2
7x2−9x−2
x2−10x+2
Answered by
GPT-4o mini
True. Polynomials are closed under addition, meaning that the sum of any two polynomials is also a polynomial.
Answered by
GPT-4o mini
The correct response is:
**NO - they are not equivalent because -(K + F) = -K + -F. I used the Distributive Property to simplify the left side.**
Justification: When applying the Distributive Property, you distribute the negative sign across the sum in the parentheses, which leads to \(-K - F\), not \(K - F\). Therefore, the two expressions are not equivalent.
**NO - they are not equivalent because -(K + F) = -K + -F. I used the Distributive Property to simplify the left side.**
Justification: When applying the Distributive Property, you distribute the negative sign across the sum in the parentheses, which leads to \(-K - F\), not \(K - F\). Therefore, the two expressions are not equivalent.
Answered by
GPT-4o mini
To find the product \( W \times G \) where \( W = 3x - 2 \) and \( G = 4x - 1 \), we will use the distributive property (also known as the FOIL method for binomials):
\[
W \times G = (3x - 2)(4x - 1)
\]
Now, we'll apply the FOIL method:
1. **First**: \( 3x \times 4x = 12x^2 \)
2. **Outer**: \( 3x \times -1 = -3x \)
3. **Inner**: \( -2 \times 4x = -8x \)
4. **Last**: \( -2 \times -1 = 2 \)
Now, combine these results:
\[
12x^2 - 3x - 8x + 2 = 12x^2 - 11x + 2
\]
Thus, the product \( W \times G \) is:
**12x² - 11x + 2**.
The correct response is:
**12x² - 11x + 2**.
\[
W \times G = (3x - 2)(4x - 1)
\]
Now, we'll apply the FOIL method:
1. **First**: \( 3x \times 4x = 12x^2 \)
2. **Outer**: \( 3x \times -1 = -3x \)
3. **Inner**: \( -2 \times 4x = -8x \)
4. **Last**: \( -2 \times -1 = 2 \)
Now, combine these results:
\[
12x^2 - 3x - 8x + 2 = 12x^2 - 11x + 2
\]
Thus, the product \( W \times G \) is:
**12x² - 11x + 2**.
The correct response is:
**12x² - 11x + 2**.