Solve the following. Subtract $\frac{9}{2} + \frac{x}{2} + \frac{3}{5}x^2 + \frac{7}{4}x^3$ from $\frac{7}{2} - \frac{x}{3} - \frac{1}{5}x^2$.
Polynomial Subtraction Steps
To solve the problem, we need to subtract the first expression from the second expression. This means we set up the subtraction as:
$ \left( \frac{7}{2} - \frac{x}{3} - \frac{1}{5}x^2 \right) - \left( \frac{9}{2} + \frac{x}{2} + \frac{3}{5}x^2 + \frac{7}{4}x^3 \right) $
Simplify the Expression
Distribute the negative sign to each term in the second expression:
$ \frac{7}{2} - \frac{x}{3} - \frac{1}{5}x^2 - \frac{9}{2} - \frac{x}{2} - \frac{3}{5}x^2 - \frac{7}{4}x^3 $
Combine Like Terms
Group and combine terms with the same power of $x$:
- Constant terms: $ \frac{7}{2} - \frac{9}{2} = \frac{7 - 9}{2} = \frac{-2}{2} = -1 $
- Terms with $x$: $ -\frac{x}{3} - \frac{x}{2} = x \left( -\frac{1}{3} - \frac{1}{2} \right) = x \left( \frac{-2 - 3}{6} \right) = -\frac{5}{6}x $
- Terms with $x^2$: $ -\frac{1}{5}x^2 - \frac{3}{5}x^2 = x^2 \left( -\frac{1}{5} - \frac{3}{5} \right) = x^2 \left( \frac{-1 - 3}{5} \right) = -\frac{4}{5}x^2 $
- Terms with $x^3$: $ -\frac{7}{4}x^3 $
Final Result
Combine the simplified terms to get the final expression:
$ -1 - \frac{5}{6}x - \frac{4}{5}x^2 - \frac{7}{4}x^3 $
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Important Questions from Polynomials
If (x + y) 3+ 8 (x - y) 3= (3x + Ay) (3x 2+ Bxy + Cy 2), then the value of A + B + C is:
Given that x 8- 34x 4+ 1 = 0, x > 0. What is the value of (x 3+ x -3 )?
If \(x - \frac 3 x = 6,\; x \ne 0,\) then the value of \(\frac {x^4 - \frac {27}{x^2}}{x^2 - 3x - 3}\) is:
If \(x\left(3 - \frac 2 x\right) = \frac 3 x,\) then the value of \(x^3 - \frac 1 {x^3}\) is equal to:
The coefficient of x in (x – 3y) 3is:
