Factorisation of Polynomials

Factorise $2y^3+y^2-2y-1$

Factorise $x^3+13x^2+32x+20$

Factorise $x^3-3x^2-9x-5$.

Factorise $6x^2+5x-6$

Factorise $3x^2-x-4$

Factorise $2x^2+7x+3$

 The value of $k$ if $x-1$ is a factor of $p\left(x\right)=k{x}^2-\sqrt{2}x+1$ is $\sqrt{2}-b$. Find the value of $b$

If the value of $k=\left(-a-\sqrt{a}\right)$ and $\left(x-1\right)$ is a factor of $p\left(x\right)=2x^2+kx+\sqrt{2}$, then find the value of $a$.

Find the value of $k$, if $\left(x-1\right)$ is a factor of $p\left(x\right)=x^2+x+k$.

Use the factor theorem to determine whether $g\left(x\right)$ is a factor of $p\left(x\right)$ in the following case: $p\left(x\right)=x^3-4x^2+x+6, g\left(x\right)=x-3$

Use the factor theorem to determine whether $g\left(x\right)$ is a factor of $p\left(x\right)$ in the following case: $p\left(x\right)=x^3+3x^2+3x+1, g\left(x\right)=x+2$
 

Check whether the following polynomial has $\left(x+1\right)$ as its factor: $x^3-x^2-\left(2+\sqrt{2}\right)x+\sqrt{2}$

Check whether the following polynomial has $\left(x+1\right)$ as its factor: $x^4+3x^3+3x^2+x+1$
 

Check whether the following polynomial has $\left(x+1\right)$ as its factor: $x^4+x^3+x^2+x+1$

Factorise $x^3-2x^2-x+2$

Factorise: $12x^2-7x+1$

Find the value of $k$ if $x-1$ is a factor of $p\left(x\right)=k{x}^2-3x+k$.

Use the factor theorem to determine whether $g\left(x\right)$ is a factor of $p\left(x\right)$ in the following case: $p\left(x\right)=2x^3+x^2-2x-1, g\left(x\right)=x+1$
 

Determine whether the following polynomial has $\left(x+1\right)$ as factor: $x^3+x^2+x+1$.