Divide the polynomials. Your answer should be a polynomial. (3x^(5)+x^(4)-4x^(2))/(x)=

Given Polynomial Division: We are given the polynomial division $(3x^5 + x^4 - 4x^2) / x$. To divide a polynomial by a monomial, we divide each term of the polynomial by the monomial.Step 1: Divide First Term: Divide the first term $3x^5$ by $x$. This gives us $3x^4$ because when we divide powers with the same base, we subtract the exponents: $5 - 1 = 4$.Step 2: Divide Second Term: Divide the second term $x^4$ by $x$. This gives us $x^3$ for the same reason as above: $4 - 1 = 3$.Step 3: Divide Third Term: Divide the third term $-4x^2$ by $x$. This gives us $-4x^1$ or simply $-4x$, again subtracting the exponents: $2 - 1 = 1$.Step 4: Combine Results: Combine the results of the divisions to get the final polynomial: $3x^4 + x^3 - 4x$.

Home

Math Problems

Algebra 2

Factor sums and differences of cubes

Full solution

Q. Divide the polynomials.

\newline

Your answer should be a polynomial.

\newline

\frac{3 x^{5}+x^{4}-4 x^{2}}{x}=

Given Polynomial Division: We are given the polynomial division $(3x^5 + x^4 - 4x^2) / x$ . To divide a polynomial by a monomial, we divide each term of the polynomial by the monomial.
Step $1$ : Divide First Term: Divide the first term $3x^5$ by $x$ . This gives us $3x^4$ because when we divide powers with the same base, we subtract the exponents: $5 - 1 = 4$ .
Step $2$ : Divide Second Term: Divide the second term $x^4$ by $x$ . This gives us $x^3$ for the same reason as above: $4 - 1 = 3$ .
Step $3$ : Divide Third Term: Divide the third term $-4x^2$ by $x$ . This gives us $-4x^1$ or simply $-4x$ , again subtracting the exponents: $2 - 1 = 1$ .
Step $4$ : Combine Results: Combine the results of the divisions to get the final polynomial: $3x^4 + x^3 - 4x$ .