Answer :
Let's solve the given polynomial problem step-by-step:
1. Given Polynomials:
We have four polynomial expressions to evaluate:
- Expression 1: [tex]\(\frac{11x^3 + 7x^3 - 2x}{x^2}\)[/tex]
- Expression 2: [tex]\(11x^3 + 7x - \frac{2}{x}\)[/tex]
- Expression 3: [tex]\(11x^3 - 7x^3 - 2x^2\)[/tex]
- Expression 4: [tex]\(11x^3 + 7x - 2x\)[/tex]
2. Simplifying Expression 1:
- First, simplify inside the numerator: [tex]\(11x^3 + 7x^3 - 2x = 18x^3 - 2x\)[/tex].
- Now, divide by [tex]\(x^2\)[/tex]: [tex]\(\frac{18x^3 - 2x}{x^2} = \frac{18x^3}{x^2} - \frac{2x}{x^2}\)[/tex].
- Simplify each term: [tex]\(\frac{18x^3}{x^2} = 18x\)[/tex] and [tex]\(\frac{2x}{x^2} = \frac{2}{x}\)[/tex].
- So, the simplified form of Expression 1 is: [tex]\(18x - \frac{2}{x}\)[/tex].
3. Expression 2:
The expression is already in its simplest form: [tex]\(11x^3 + 7x - \frac{2}{x}\)[/tex].
4. Simplifying Expression 3:
- Simplify inside the expression: [tex]\(11x^3 - 7x^3 - 2x^2 = 4x^3 - 2x^2\)[/tex].
- You can factor out [tex]\(x^2\)[/tex]: [tex]\(x^2(4x - 2)\)[/tex].
- So, the simplified form of Expression 3 is: [tex]\(x^2(4x - 2)\)[/tex].
5. Simplifying Expression 4:
- Simplify inside the expression: [tex]\(11x^3 + 7x - 2x = 11x^3 + 5x\)[/tex].
- You can factor out [tex]\(x\)[/tex]: [tex]\(x(11x^2 + 5)\)[/tex].
- So, the simplified form of Expression 4 is: [tex]\(x(11x^2 + 5)\)[/tex].
In summary, here are the simplified forms of the expressions:
- Expression 1: [tex]\(18x - \frac{2}{x}\)[/tex]
- Expression 2: [tex]\(11x^3 + 7x - \frac{2}{x}\)[/tex]
- Expression 3: [tex]\(x^2(4x - 2)\)[/tex]
- Expression 4: [tex]\(x(11x^2 + 5)\)[/tex]
1. Given Polynomials:
We have four polynomial expressions to evaluate:
- Expression 1: [tex]\(\frac{11x^3 + 7x^3 - 2x}{x^2}\)[/tex]
- Expression 2: [tex]\(11x^3 + 7x - \frac{2}{x}\)[/tex]
- Expression 3: [tex]\(11x^3 - 7x^3 - 2x^2\)[/tex]
- Expression 4: [tex]\(11x^3 + 7x - 2x\)[/tex]
2. Simplifying Expression 1:
- First, simplify inside the numerator: [tex]\(11x^3 + 7x^3 - 2x = 18x^3 - 2x\)[/tex].
- Now, divide by [tex]\(x^2\)[/tex]: [tex]\(\frac{18x^3 - 2x}{x^2} = \frac{18x^3}{x^2} - \frac{2x}{x^2}\)[/tex].
- Simplify each term: [tex]\(\frac{18x^3}{x^2} = 18x\)[/tex] and [tex]\(\frac{2x}{x^2} = \frac{2}{x}\)[/tex].
- So, the simplified form of Expression 1 is: [tex]\(18x - \frac{2}{x}\)[/tex].
3. Expression 2:
The expression is already in its simplest form: [tex]\(11x^3 + 7x - \frac{2}{x}\)[/tex].
4. Simplifying Expression 3:
- Simplify inside the expression: [tex]\(11x^3 - 7x^3 - 2x^2 = 4x^3 - 2x^2\)[/tex].
- You can factor out [tex]\(x^2\)[/tex]: [tex]\(x^2(4x - 2)\)[/tex].
- So, the simplified form of Expression 3 is: [tex]\(x^2(4x - 2)\)[/tex].
5. Simplifying Expression 4:
- Simplify inside the expression: [tex]\(11x^3 + 7x - 2x = 11x^3 + 5x\)[/tex].
- You can factor out [tex]\(x\)[/tex]: [tex]\(x(11x^2 + 5)\)[/tex].
- So, the simplified form of Expression 4 is: [tex]\(x(11x^2 + 5)\)[/tex].
In summary, here are the simplified forms of the expressions:
- Expression 1: [tex]\(18x - \frac{2}{x}\)[/tex]
- Expression 2: [tex]\(11x^3 + 7x - \frac{2}{x}\)[/tex]
- Expression 3: [tex]\(x^2(4x - 2)\)[/tex]
- Expression 4: [tex]\(x(11x^2 + 5)\)[/tex]
