Algebraic Polynomials & Identities Questions with Solutions

If $p\left(x\right)=x^2-2\sqrt{2}x+1$, then $p\left(2\sqrt{2}\right)$ is equal to

What should be subtracted from $5y-13x-8a$ to obtain $11x-16y+7a$?

The remainder, when $3x^3-2x^{2}y-13x{y}^2+10y^3$ is divided by $\left(x-2y\right)$, is equal to

If $x=2-p$, then $x^3+6xp+p^3$ is equal to

If $x=2,y=1,z=-3$, then $x^3+y^3+z^3-3xyz$ equals

The value of $\frac{{\left(x-y\right)}^3+{\left(y-z\right)}^3+{\left(z-x\right)}^3}{9\left(x-y\right)\left(y-z\right)\left(z-x\right)}$ is

Which of the following is a zero of the polynomial $3x^3+4x^2-7$?

For $a=-5$ and $b=5$, the value of $a^2-b^2$ is

What is the value of $8x^3+18xy+y^3-27$, when $2x+y-3=0$?

If the highest common factor of $x^2-px-q$ and $5x^2-3px-15q$ is $\left(x-3\right)$, then the values of $p$ and $q$ will be

What is the square root of $\left(x^2-14x+49\right)\left(x^2+6x+9\right)$?

If $x+y=4$ and $\frac{1}{x}+\frac{1}{y}=\frac{16}{15}$, then what is the value of $\left(x^3+y^3\right)$?

If $x,y,z$ are positive integers such that $x:y=1:2$ and $y:z=3:5$, then which one of the following will be a possible value of $5x-3y+z$?

What is the simplified value of $\frac{1}{8}\left\{{\left(x+\frac{1}{y}\right)}^2-{\left(x-\frac{1}{y}\right)}^2\right\}$?

If $x^2+\left(4-\sqrt{3}\right)x-1=0$, then what is the value of $x^2+\frac{1}{x^2}$?

If $x+\frac{1}{x}=\sqrt{13}$, then one of the values of $x^3-\frac{1}{x^3}$ is

What is the value of $a\left(a+b^2+c\right)+b^2\left(a^2+b^2+c^2\right)-c\left(a+b^2\right)$, when $a=1$, $b=-3$ and $c=-2$?

If ${\left(3x-1\right)}^3+{\left(4x-3\right)}^3+{\left(2x+1\right)}^3=3\left(3x-1\right)\left(4x-3\right)\left(2x+1\right)$ and $x\ne \frac{1}{3}$, then $x=?$

If $x^3+y^3=468$ and $x+y=12$, then the value of $x^4+y^4$ will be

If $a+b+c=11$, $ab+bc+ca=3$ and $abc=-135$, then what is the value of $a^3+b^3+c^3$?