To simplify the given expression [tex]\[ 2x + 6x^2 - 10 + 4x^2 - 3x + (-6) \][/tex], we need to combine like terms. Here is the step-by-step solution:
1. Identify and group the like terms:
- Terms with [tex]\( x^2 \)[/tex]: [tex]\( 6x^2 \)[/tex], [tex]\( 4x^2 \)[/tex]
- Terms with [tex]\( x \)[/tex]: [tex]\( 2x \)[/tex], [tex]\( -3x \)[/tex]
- Constant terms: [tex]\( -10 \)[/tex], [tex]\( -6 \)[/tex]
2. Combine the [tex]\( x^2 \)[/tex] terms:
[tex]\[
6x^2 + 4x^2 = 10x^2
\][/tex]
3. Combine the [tex]\( x \)[/tex] terms:
[tex]\[
2x - 3x = -x
\][/tex]
4. Combine the constant terms:
[tex]\[
-10 + (-6) = -16
\][/tex]
5. Write the simplified expression:
[tex]\[
10x^2 - x - 16
\][/tex]
So, the simplified expression is [tex]\( 10x^2 - x - 16 \)[/tex]. Among the given choices, the correct answer is:
[tex]\[ 10x^2 - x - 16 \][/tex]
