Question
Write the polynomial expression in simplest form: 6xx−4⋅x2−164x+16
.(1 point)
Responses
3x2
Start Fraction 3 x over 2 End Fraction
6x4
Start Fraction 6 x over 4 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
3x2
Start Fraction 3 x over 2 End Fraction
6x4
Start Fraction 6 x over 4 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 write the polynomial expression \( 6x^2 - 4 \cdot (x^2 - 16) \) in simplest form, we start by distributing and simplifying.
1. Distribute \(-4\):
\[
-4 \cdot (x^2 - 16) = -4x^2 + 64
\]
2. Substitute this back into the expression:
\[
6x^2 - 4x^2 + 64
\]
3. Combine like terms:
\[
(6x^2 - 4x^2) + 64 = 2x^2 + 64
\]
4. Factor out the common factor of \(2\):
\[
2(x^2 + 32)
\]
Now, we compare this with the provided options:
1. \(3x^2\)
2. \(\frac{3x}{2}\)
3. \(\frac{6x(x + 4)}{4(x - 4)}\)
4. \(3x(x + 4)^2(x - 4)\)
The expression \(2(x^2 + 32)\) does not match any of the options directly. It is possible that the question format was misinterpreted. If you require further steps or clarification, feel free to ask!
1. Distribute \(-4\):
\[
-4 \cdot (x^2 - 16) = -4x^2 + 64
\]
2. Substitute this back into the expression:
\[
6x^2 - 4x^2 + 64
\]
3. Combine like terms:
\[
(6x^2 - 4x^2) + 64 = 2x^2 + 64
\]
4. Factor out the common factor of \(2\):
\[
2(x^2 + 32)
\]
Now, we compare this with the provided options:
1. \(3x^2\)
2. \(\frac{3x}{2}\)
3. \(\frac{6x(x + 4)}{4(x - 4)}\)
4. \(3x(x + 4)^2(x - 4)\)
The expression \(2(x^2 + 32)\) does not match any of the options directly. It is possible that the question format was misinterpreted. If you require further steps or clarification, feel free to ask!