Question
Write the polynomial expression in simplest form: 6xx−4⋅x2−164x+16
.(1 point)
Responses
6x4
Start Fraction 6 x over 4 End Fraction
3x2
Start Fraction 3 x over 2 End Fraction
6x(x+4)4(x−4)
Start Fraction 6 x left parenthesis x plus 4 right parenthesis over 4 left parenthesis x minus 4 right parenthesis End Fraction
3x(x+4)2(x−4)
.(1 point)
Responses
6x4
Start Fraction 6 x over 4 End Fraction
3x2
Start Fraction 3 x over 2 End Fraction
6x(x+4)4(x−4)
Start Fraction 6 x left parenthesis x plus 4 right parenthesis over 4 left parenthesis x minus 4 right parenthesis End Fraction
3x(x+4)2(x−4)
Answers
GPT-4o mini
To simplify the expression \( 6xx - 4 \cdot x^2 - 164x + 16 \), we first rewrite it clearly using standard notation.
1. Notice that \( xx \) is the same as \( x^2 \), so rewrite the expression:
\[
6x^2 - 4x^2 - 164x + 16
\]
2. Combine like terms:
\[
(6x^2 - 4x^2) - 164x + 16 \Rightarrow 2x^2 - 164x + 16
\]
3. Next, we can factor out a common factor from the quadratic expression \( 2x^2 - 164x + 16 \):
\[
2(x^2 - 82x + 8)
\]
4. To simplify further, we will focus on the quadratic \( x^2 - 82x + 8\). We can try factoring or using the quadratic formula to find its roots.
Since the polynomial doesn't factor easily, and because we're asked for the simplest form, we might want to use the roots, but it’s likely faster to rewrite it as is.
Now we look at your answer choices:
- The expression \( 3x(x + 4)^2(x - 4) \) seems to suggest some factorization that we haven't stripped down to as basic forms given that it's not obvious from our steps.
Given that this is the simplest polynomial, the correct formatted answer in simplest terms would be:
\[
\boxed{2(x^2 - 82x + 8)}
\]
Since none of the answer choices directly match, check to confirm the responses you've provided or clarify additional context—if any specific factors were assumed earlier.
1. Notice that \( xx \) is the same as \( x^2 \), so rewrite the expression:
\[
6x^2 - 4x^2 - 164x + 16
\]
2. Combine like terms:
\[
(6x^2 - 4x^2) - 164x + 16 \Rightarrow 2x^2 - 164x + 16
\]
3. Next, we can factor out a common factor from the quadratic expression \( 2x^2 - 164x + 16 \):
\[
2(x^2 - 82x + 8)
\]
4. To simplify further, we will focus on the quadratic \( x^2 - 82x + 8\). We can try factoring or using the quadratic formula to find its roots.
Since the polynomial doesn't factor easily, and because we're asked for the simplest form, we might want to use the roots, but it’s likely faster to rewrite it as is.
Now we look at your answer choices:
- The expression \( 3x(x + 4)^2(x - 4) \) seems to suggest some factorization that we haven't stripped down to as basic forms given that it's not obvious from our steps.
Given that this is the simplest polynomial, the correct formatted answer in simplest terms would be:
\[
\boxed{2(x^2 - 82x + 8)}
\]
Since none of the answer choices directly match, check to confirm the responses you've provided or clarify additional context—if any specific factors were assumed earlier.