# Give a polynomial division that has a quotient of x+5 and a remainder of -2.

Question
Polynomial factorization
Give a polynomial division that has a quotient of x+5 and a remainder of -2.

2021-01-11
Step 1
The quotient is x+5 and the remainder is -2
By using the formula,
Polynomial = Divisor $$\displaystyle\times$$ Quotient + Remainder
Take divisor = x + 1
Thus, the polynomial is
Polynomial $$\displaystyle={\left({x}+{1}\right)}\times{\left({x}+{5}\right)}+{\left(-{2}\right)}$$
Polynomial $$\displaystyle={x}^{{2}}+{6}{x}+{5}-{2}$$
Polynomial $$\displaystyle={x}^{{2}}+{6}{x}+{3}$$
Step 2
By using the polynomial division,
$$\displaystyle\frac{{{x}^{{2}}+{6}{x}+{3}}}{{{x}+{1}}}$$
The first term is x2 so the first term in the quotient is x
$$\displaystyle{x}{\left({x}+{1}\right)}={x}^{{2}}+{x}$$
So, $$\displaystyle{x}^{{2}}+{6}{x}+{3}-{\left({x}^{{2}}+{x}\right)}={5}{x}+{3}$$
Now if 5x + 3 divide by x +1 then the quotient is x
5(x+1) = 5x + 5
So, 5x + 3 - (5x + 5) = -2 (This is the remainder)
The quotient is x+5 and remainder is -2
Hence, the solution

### Relevant Questions

When $$2x^{2}-7+9$$ is divided by a polynomial, the quotient is 2x - 3 and the remainder is 3. Find the polynomial?

Use long division to rewrite the equation for g in the form
$$\text{quotient}+\frac{remainder}{divisor}$$
Then use this form of the function's equation and transformations of
$$\displaystyle{f{{\left({x}\right)}}}={\frac{{{1}}}{{{x}}}}$$
to graph g.
$$\displaystyle{g{{\left({x}\right)}}}={\frac{{{2}{x}+{7}}}{{{x}+{3}}}}$$

Discuss the following situation by computation or proving. Make sure to show your complete solution.
Give a polynomial division that has a quotient of x+5 and a remainder of -2.
Give a polynomial division that has a quotient of x+5 and a remainder of -2
Discuss the following situation by computation or proving.
Make sure to show your complete solution.
Give a polynomial division that has a quotient of $$x+5$$ and a remainder of -2.
Discuss the following situation by computation or proving. Make sure to show your complete solution. Give a polynomial division that has a quotient of $$x+5$$ and a remainder of -2.
Consider the polynomial function $$p(x)=(3x^{2}-5x-2)(x-5)(x^{2}-4)$$.
A) what is the degree of the polynomial? What is the y intercept of the function?
B)What are the zeros and their multiplicities?
C) what is the leading term of the polynomial and what power function has a graph most similiar to the graph of p?
A given polynomial has a root of x = 3, an zero of x = -2, and an x-intercept of x = -1.
The equation of this polynomial in factored form would be f(x) =
The equation of this polynomial in standard form would be f(x) =
$$\text{quotient}+\frac{remainder}{divisor}$$
$$\displaystyle{f{{\left({x}\right)}}}={\frac{{{1}}}{{{x}}}}$$
$$\displaystyle{g{{\left({x}\right)}}}={\frac{{{3}{x}-{7}}}{{{x}-{2}}}}$$
$$\displaystyle{x}\equiv{5}{\left({b}\text{mod}{24}\right)}$$
$$\displaystyle{x}\equiv{17}{\left({b}\text{mod}{18}\right)}$$