R Chandra Solutions for Chapter: Polynomials, Exercise 5: TEST YOUR SKILLS

Factorise: ${(\mathrm{p}-\mathrm{q})}^3+{(\mathrm{q}-\mathrm{r})}^3+{(\mathrm{r}-\mathrm{p})}^3$.

What is the degree of the polynomial: $(\mathrm{x}-1)(\mathrm{x}+1)(\mathrm{x}-2)$?

Find the value of polynomial: $7\mathrm{y}-4{\mathrm{y}}^2+5\hspace{0.17em}$ at $\hspace{0.17em}\hspace{0.17em}\mathrm{y}=-1$.

When the polynomial $6{\mathrm{x}}^3+11{\mathrm{x}}^2-12\mathrm{x}-\mathrm{a}$ and $3{\mathrm{x}}^3+{\mathrm{x}}^2-12\mathrm{x}-2$ are divided by $\left(3\mathrm{x}+1\right)$ then remainder is same. Find the value of $\mathrm{‘}\mathrm{a}\mathrm{’}$.

If one zero of $4{\mathrm{x}}^3-20{\mathrm{x}}^2+27\mathrm{x}-9$ is 3, find the other zeroes of the polynomial.

If the polynomials $\mathrm{a}{\mathrm{x}}^3+3{\mathrm{x}}^2-13\hspace{0.17em}\hspace{0.17em}$and $\hspace{0.17em}\hspace{0.17em}2{\mathrm{x}}^3-5\mathrm{x}+\mathrm{a}$ are divided by $(\mathrm{x}–2)$, the remainder is same. Find the value of $\mathrm{a}$.

If $\mathrm{x}+\mathrm{y}=5\mathrm{}$ and $\mathrm{}\mathrm{x}\mathrm{y}=4$, Find ${\mathrm{x}}^3+{\mathrm{y}}^3$.

Factorise: $27{\mathrm{a}}^3-64{\mathrm{b}}^3-108{\mathrm{a}}^2\mathrm{b}+144\mathrm{a}{\mathrm{b}}^2+9\mathrm{a}-12\mathrm{b}$