 # Polynomials questions and answers

Recent questions in Polynomials Medenovgj 2022-09-26

### Given that $\left(x-1\right)$ is a factor of ${x}^{3}+3{x}^{2}+x-5$, factorize this cubic fully. Melina Barber 2022-09-25

### Let ${a}_{1},\dots ,{a}_{n}$ be points on the unit circle. Let $P\left(z\right)=\left(z-{a}_{1}\right)\cdots \left(z-{a}_{n}\right)$. Prove that there exists a point b on the unit circle such that $|P\left(b\right)|=1$ Orion Cervantes 2022-09-25

### Find the coefficient of ${x}^{8}$ in the polynomial $\left(x-1\right)\left(x-2\right)\cdots \cdots \left(x-10\right)$ besnuffelfo 2022-09-24

### Find the polynomial $p\left(x\right)={x}^{2}+px+q$ for which $max\left\{\phantom{\rule{mediummathspace}{0ex}}|p\left(x\right)|\phantom{\rule{mediummathspace}{0ex}}:\phantom{\rule{mediummathspace}{0ex}}x\in \left[-1,1\right]\phantom{\rule{mediummathspace}{0ex}}\right\}$ is minimal. ye1neh4 2022-09-23

### Given the polynomial $\left(x-1\right)\left(x-8\right)\left(x-31\right)-1$, how do you conclude that its roots are irrational? Haiphongum 2022-09-23

### What is the process of solving an equation with the square and the 4th power of an unknown, for example ${x}^{4}-6{x}^{2}-27=0$ Jazmyn Pugh 2022-09-22

### How find this $\sum _{k=0}^{2n}\left(-1{\right)}^{k}{a}_{k}^{2}$ Gillian Cooper 2022-09-22

### If $a,b$ and c are the roots of ${x}^{3}+p{x}^{2}+qx+r$, then how can we find the value of $\sum \frac{{b}^{2}+{c}^{2}}{bc}$ Chelsea Lamb 2022-09-20

### If I have a polynom p with $p\left(a\right)=0$, how to construct a polynom q with $q\left({a}^{-1}\right)=0$ memLosycecyjz 2022-09-20

### I have this polynomials: $f={x}^{4}+3{x}^{3}+{x}^{2}+3\in {\mathbb{Z}}_{5}\left[x\right]$, $g=x+2\in {\mathbb{Z}}_{5}\left[x\right]$ saucletbh 2022-09-18

### Prove that ${x}_{1}^{n}+{x}_{2}^{n}$ is an integer and is not divisible by 5 Zachariah Norris 2022-09-18

### Find the multiplicative inverse of $\phantom{\rule{thinmathspace}{0ex}}{x}^{2}+\left({x}^{3}-x+2\right)$ in the quotient $\phantom{\rule{thinmathspace}{0ex}}{F}_{3}\left[x\right]/\left({x}^{3}-x+2\right)$ mikioneliir 2022-09-18

### Define Bernoulli polynomials as: ${P}_{n}^{\prime }\left(x\right)=n{P}_{n-1}\left(x\right)$, ${\int }_{0}^{1}{P}_{n}\left(x\right)=0$ if$n\ge 1$ Zack Chase 2022-09-18

### Suppose I have a cubic equation of${x}^{3}+a{x}^{2}+bx+c=0.$What steps would one take to eliminate the ${x}^{2}$ term? Urraiyg 2022-09-18

### Express $\frac{1}{x+4}-\frac{1}{x+7}$ as a single reduced fraction $\frac{N\left(x\right)}{D\left(x\right)}$ where N(x) and D(x) are polynomials in x. Orion Cervantes 2022-09-17

### If a and b are the roots of the equation$2{x}^{2}-px+7=0$Then a-b is a root of ? madeeha1d8 2022-09-17

### List all possible rational zeros of the polynomial function:$f\left(x\right)={x}^{4}+2{x}^{3}-3{x}^{2}+2x+6$ sincsenekdq 2022-09-16

### Second - degree, with zeros of -1 -1 and 66, and goes to $-\mathrm{\infty }-\mathrm{\infty }$ as $x\to -\mathrm{\infty }$ furajat4h 2022-09-15
### Suppose we have a polynomial satisfying $p+{p}^{‴}\ge {p}^{\prime }+{p}^{″}$ for all x. Then prove that $p\left(x\right)\ge 0$ for all x. curukksm 2022-09-05