Write the polynomial expression in simplest form: 6xx−4⋅x2−164x+16

Question

.(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)

Answer 1

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!