Answer :
To simplify the expression [tex]\(\frac{2x^2 - 6x^3}{2x^2}\)[/tex], follow these steps:
1. Look at the expression: You have [tex]\(\frac{2x^2 - 6x^3}{2x^2}\)[/tex].
2. Factor out the common factor in the numerator: Notice that [tex]\(2x^2\)[/tex] is a common factor in the numerator. So you can factor [tex]\(2x^2\)[/tex] out of the numerator:
[tex]\[
2x^2 - 6x^3 = 2x^2(1 - 3x)
\][/tex]
3. Rewrite the expression with the factored numerator:
[tex]\[
\frac{2x^2(1 - 3x)}{2x^2}
\][/tex]
4. Cancel the common factor [tex]\(2x^2\)[/tex] in the numerator and the denominator: Since [tex]\(2x^2\)[/tex] is present in both the numerator and the denominator, you can cancel it out:
[tex]\[
\frac{2x^2(1 - 3x)}{2x^2} = 1 - 3x
\][/tex]
So, the simplified expression is [tex]\(1 - 3x\)[/tex].
None of the given options (A, B, C, D) match the simplified expression [tex]\(1 - 3x\)[/tex], which indicates something might be incorrect with the answering options or they don't represent this particular problem outcome. The correct simplified form of the expression is [tex]\(1 - 3x\)[/tex].
1. Look at the expression: You have [tex]\(\frac{2x^2 - 6x^3}{2x^2}\)[/tex].
2. Factor out the common factor in the numerator: Notice that [tex]\(2x^2\)[/tex] is a common factor in the numerator. So you can factor [tex]\(2x^2\)[/tex] out of the numerator:
[tex]\[
2x^2 - 6x^3 = 2x^2(1 - 3x)
\][/tex]
3. Rewrite the expression with the factored numerator:
[tex]\[
\frac{2x^2(1 - 3x)}{2x^2}
\][/tex]
4. Cancel the common factor [tex]\(2x^2\)[/tex] in the numerator and the denominator: Since [tex]\(2x^2\)[/tex] is present in both the numerator and the denominator, you can cancel it out:
[tex]\[
\frac{2x^2(1 - 3x)}{2x^2} = 1 - 3x
\][/tex]
So, the simplified expression is [tex]\(1 - 3x\)[/tex].
None of the given options (A, B, C, D) match the simplified expression [tex]\(1 - 3x\)[/tex], which indicates something might be incorrect with the answering options or they don't represent this particular problem outcome. The correct simplified form of the expression is [tex]\(1 - 3x\)[/tex].
