If when adding three polynomials, P+Q+R the result is $2{x}^{2}y$ and the polynomials P and Q are given by the expressions $P={x}^{3}+5x{y}^{2}+{y}^{3},Q={y}^{3}-10x{y}^{2}-{x}^{3}$ . What is the expression for the polynomial R?

geduiwelh
2021-09-04
Answered

If when adding three polynomials, P+Q+R the result is $2{x}^{2}y$ and the polynomials P and Q are given by the expressions $P={x}^{3}+5x{y}^{2}+{y}^{3},Q={y}^{3}-10x{y}^{2}-{x}^{3}$ . What is the expression for the polynomial R?

You can still ask an expert for help

casincal

Answered 2021-09-05
Author has **82** answers

Solution of the problem as follows

We have given three polynomials

$P={x}^{3}+5x{y}^{2}+{y}^{3}$

$Q={y}^{3}-10x{y}^{2}-{x}^{3}$

and$P+Q+R=2{x}^{2}y$

Then we have to final R.

$\Rightarrow P+Q+R=2{x}^{2}y$

$\Rightarrow {x}^{3}+{y}^{3}+5x{y}^{2}+{y}^{3}-{x}^{3}-10x{y}^{2}+R=2{x}^{2}y$

$\Rightarrow R=2{x}^{2}y-2{y}^{3}+5x{y}^{2}$

We have given three polynomials

and

Then we have to final R.

asked 2020-10-28

Find a polynomial with integer coefficients that satisfies the given conditions. Q has degree 3 and zeros 0 and i.

asked 2021-02-25

Find a polynomial of the specified degree that has the given zeros. Degree 4, zeros -2, 0, 2, 4

asked 2022-03-22

Suppose that a polynomial function of degree 4 with rational coefficient has the given number as zeros . Find the other zeros.

-1, √3, 11/3

asked 2021-09-09

Let $f\left(x\right)={x}^{3}+{x}^{2}+x+1\in {Z}_{2}\left[x\right]$ . Write f(x) as a product of irreducible polynomials over $Z}_{2$

asked 2021-09-15

Add the given polynomials.

$3{x}^{2}-5x-1$ and $-4{x}^{2}+7x-1$

asked 2022-04-30

Factor $${y}^{2}\ufeff+5y+6$$.

asked 2022-04-26

Simplifying

$1-x+{x}^{2}-{x}^{3}+\dots +{x}^{98}-{x}^{99}$ to an equivalent expression.